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Opportunistic Scheduling: An Illustration of Cross-layer Design Xin Liu Ness B. Shroff Edwin K. P. Chong Computer Science Dept. Dept. of Electrical & Computer Engineering Dept. of Electrical & Computer Engineering Univ. of California, Davis Purdue University Colorado State University Abstract losses. 2) Transport layer and network layer, e.g., TCP modifications for energy efficiency. 3) Network layer and data link layer. For instance, link reliability The unique characteristics of wireless information can facilitate routing decisions. 4) MAC communication systems - namely, timing-varying and physical layer, which is the focus of this paper. channel conditions and multiuser diversity - call for specifically tailored system designs. In this paper, we The basic idea of ―opportunistic scheduling‖ that will overview a cross-layer design method, named be overviewed in this paper is allocating resources to opportunistic scheduling, for exploiting the time- links when they experience good channel conditions varying nature of the radio environment to increase while avoiding allocating resources to links when the overall performance of the system under certain they experience poor channel conditions, thus QoS/fairness requirements of users. We first discuss efficiently utilizing radio resources. This is also a general system model, and the fairness and QoS referred to as channel-aware scheduling or exploiting constraints being considered. Then, we present multi-user diversity. We use the term opportunistic various optimal index policies and discuss their to denote the ability to schedule users based on properties. We also outline a methodology to favorable channel conditions. On the other hand, the implement these opportunistic scheduling solutions potential to transmit at higher data rates in practice. Lastly, we discuss the advantages and opportunistically (i.e., when channel conditions costs associated with opportunistic scheduling, and permit) also introduces an important tradeoff between identify possible future research directions. wireless resource efficiency and the level of satisfaction among different users. For example, allowing only users close to the base station to 1. Introduction and Literature Review transmit at high transmission power may result in Built upon the success of the second generation very high throughput, but sacrifice the transmissions cellular services, tremendous amounts of resources of other users. Such a scheme cannot satisfy the have been invested into 3G systems, especially in increasing demand for quality of service (QoS) Asia, by companies such as SK Telcom and NTT provisioning in the emerging high-rate data wireless DoCoMo. Furthermore, other wireless systems, networks. To address this problem, we present here a including WLAN, ad-hoc networks, and wireless framework for scheduling users in an opportunistic sensor networks, are rapidly proliferating. In way. The objective is to improve wireless resource summary, the demand for wireless data services is efficiency by exploiting time-varying channel skyrocketing and there is a real need to optimally conditions while at the same time controlling the design and engineer wireless systems.A major level of fairness and QoS among users. challenge is that wireless communication requires 1.1 Literature Review sharing a limited natural resource: the radio frequency spectrum. The data-rate capacity that a Wireless scheduling schemes have attracted a lot of radio frequency channel can support is limited by recent attention. First, the scheduling policies of Shannon’s capacity laws. Hence, in the wireless wireline networks are extended to wireless networks. environment, one has to engineer the network very The proposed wireless scheduling schemes provide carefully so that little, if any, wireless spectrum is various degrees of performance guarantees, including wasted. short-term and long-term fairness, as well as short- term and long-term throughput bounds. A survey of Compared with the wired counterpart, wireless these algorithms can be found in [1]. However, these systems have some unique characteristics, namely efforts model a channel as being either ―good‖ or scarce resource, time-varying and location dependent ―bad,‖ which may be too simple to effectively channel conditions. The nature of the wireless characterize realistic wireless channels, especially for medium makes it particularly attractive for cross- data services. layer design. Different layers have been considered, as illustrated by the following examples. 1) In [2, 3], the authors present a scheduling scheme for Application layer and network layer. For instance, a the Qualcomm/HDR system. Their scheduling multimedia server can adjust the coding scheme scheme exploits time-varying channel conditions based on available bandwidth by tracking packet while maintaining ―proportional fairness,‖ as defined in [3, 4]. conclusion in Section 5. All the results are presented without proofs. We refer readers to the corresponding In [5, 6, 7, 8], the authors study scheduling papers for reference. algorithms where both delay and channel conditions are taken into account. Throughput optimality is 2. System Model and Constraints defined in [6] as follows: a scheduling algorithm is 2.1 System Model throughput optimal if it is able to keep all queues stable if this is at all feasible to do with any We consider a time-slotted system where time is the scheduling algorithm. Furthermore, the authors of [9] resource to be shared among all users. The system investigate a scheduling algorithm to maximize the can have more than one channel (frequency band), minimum weighted throughput of users. We discuss but at any given time, only one user can occupy a these schemes in more detail later. given channel within a cell. Here, we focus on the scheduling problem for a single given channel. Such In [10, 11], we present a framework for opportunistic a system model includes TDMA systems as well as scheduling. In particular, the overall performance of time-slotted CDMA systems. An example of the the system is maximized under certain QoS/fairness latter is the IS-856 system, also known as HDR, requirements of users. where each time slot is 1.67ms. Opportunistic scheduling exploits the channel Channel conditions in wireless networks are time- fluctuations of users. Thus a natural question to ask is varying, and thus users experience time-varying what we should do in environments with little performance. We use a stochastic model to capture scattering and/or slow fading. In [12], the authors the time-varying and channel-condition-dependent present a scheme that uses multiple transmission performance of each user. Specifically, following the antennas to ―induce‖ channel fluctuations, and thus k exploit multi-user diversity. Further, such a scheme approach of [12], let {U i } be a stochastic process can also be used opportunistically to null inter-cell interference. associated with user i , where U ik is the level of performance that would be experienced by user i if In [13], scheduling problems for real-time traffic are k studied. The authors show that the greedy algorithm it is scheduled to transmit at time k. The value of U i is 1/2 competitive against the offline optimal measures the ―worth‖ or ―utility‖ of time-slot k to the algorithm. Furthermore, they show that no user i, and is in general a function of its channel deterministic online algorithm can achieve a condition. The better the channel condition of user i, competitive ratio higher than 1/2. k the larger the value of U i . Examples of the value of Opportunistic scheduling has also been studied under various scenarios, including distributed systems, U ik are throughput, the value of throughput minus (e.g., [14, 15, 16],) systems with multiple input and the cost of power consumption, etc. We assume that multiple output (MIMO) antenna arrays, (e.g., [17, U ik is nonnegative and bounded. For simplicity, we 18, 12],) multi-carrier systems, (e.g., [19],) sensor k networks, (e.g., [20],) multi-hop wireless systems, assume that {U i } is stationary and ergodic (this (e.g., [21, 22],) and with power and rate control, (e.g., assumption can be removed in some case, e.g., see [23, 24, 25]). A cautionary note on cross-layer design [11]). For convenience, we use the notation is presented in [26]. A thorough analysis on user – level performance is given in [27]. U {U1 ,,U N }, where U i is a random variable representing the performance value of user i 1.2 Organization at a generic time-slot, and N is the number of users. This paper overviews the concept of opportunistic Note that the stationary assumption does not preclude scheduling and how it can be used to improve system correlations across users or across time and moreover efficiency as well as provide adequate QoS. In this assumption can be relaxed, as in [11]. Section 2, we provide a general system model, and Wireless spectrum is a scarce resource, hence the fairness and QoS constraints being considered. improving the efficiency of spectrum utilization is Then, in Section 3, we present various optimal index important, especially to provide affordable high-rate- policies and discuss their properties. In Section 3, we data service. However, a scheme designed only to also outline a methodology of how to implement maximize the overall throughput could be unfairly these opportunistic scheduling solutions in practice. biased, especially when there are users with widely In Section 4 we provide a discussion of various issues disparate distances from the base station. To address as well as some precautionary notes and possible this problem, we introduce QoS/fairness future research directions. This is followed by a requirements into the framework of opportunistic scheduling— our goal is to maximize the system objective is to maximize the overall system performance (defined later) by exploiting time- throughput regardless the performance of each varying channel conditions while maintaining certain individual user. In other words, each user is user-oriented constraints. Examples of such guaranteed zero percent of the system throughput. In constraints include long-term and/or short-term this case, a small number of users with very good fairness constraints or (direct) performance channel conditions may consume all the resource and constraints. starve other users. A scheduling policy is a rule that specifies which user Max-min fairness The objective of the throughput is scheduled at each time-slot. For simplicity of max-min fairness is to maximize the minimum throughput of all users. Let N be the number of users notation, let Q (U ) be the decision of a stationary in the system. Each user is guaranteed 1/N portion of policy Q at a general time-slot where U is the the system throughput. This objective is ―absolutely‖ performance value of users. At a generic time-slot, if fair. However, when there are users with very poor channel conditions, to achieve max-min throughput a policy Q schedules user i Q(U ) {1,..., N } fairness will cause significant system performance to transmit, then the system receives a ―reward‖ of penalty. U i . Note that E(UQ (U ) ) is the average system Proportional fairness: Proportional fairness (PF) performance value associated with policy Q, and it is scheduler maximizes the product of the throughput the sum of all users’ average performance values delivered to all the users. In other words, the set of (where we reap a reward of U i only if user i is throughput achieved by different users is proportionally fair if increasing the throughput of one scheduled). The objective is to find a policy Q that user from the current level by x% requires a maximizes the average system performance value cumulative percentage decrease in all the users of E(UQ(U ) ) under the constraints. In this paper, we more than x%. Proportional fairness presents a focus on stationary policies. Extensions on more tradeoff between the overall throughput and each general policies, including non-stationary and non- user’s throughput. causal policies, can be found in [11]. Temporal resource-sharing fairness: In this case, We are interested only in policies that satisfy specific each user is guaranteed a certain portion of the QoS/fairness requirements. We say that a policy Q is resource, i.e., time-slots. Note that temporal resource- feasible if it satisfies the constraints for all users. Our sharing fairness is different from the utilitarian goal is to find a feasible policy Q that maximizes the fairness. In wireline networks, when a certain amount system performance, which may be defined of resource is assigned to a user, it is equivalent to differently under different assumptions. granting the user a certain amount of throughput/performance value. However, the We focus on the downlink of a wireless network. The situation is different in wireless networks, where the base station serves as the scheduling agent. The amount of resource and the performance value are scheduling scheme does the following: at the not directly related (though closely correlated). By beginning of a time-slot, the scheduler (i.e., the base limiting the resource of each individual user, a user is station) decides which user should be assigned the guaranteed a certain throughput (based on its channel time-slot based on the performance values of the conditions). Resource consumed by a user can be users at that time-slot. If a user is assigned a time- directly connected with the price the user should pay. slot, then the base station will transmit to the user in Premium users will obtain better services in a that time-slot. In general, downlink transmission is stochastic sense. more important for data traffic because of the highly asymmetric nature of the data service. Minimum data-rate constraints: In this case, each user is guaranteed a minimum data-rate. This type of 2.2 Fairness and QoS Constraints QoS constraint is desirable for users, but difficult for the system where feasibility is a major concern. We first summarize the fairness and QoS constraints discussed in the paper. 3. Optimal Scheduling Policies Utilitarian fairness: In this case, each user is A common objective of opportunistic scheduling is to guaranteed a certain portion of the total system maximize the system performance given the throughput. Two extreme cases of utilitarian fairness fairness/QoS constraints. To maximize the system is the max-min throughput fairness and system performance is formally presented as throughput maximization. max Q E(U Q(U ) ) . Throughput maximization In this case, the only Ti (Q) E(Ui 1{Q(U ) i}) be the throughput : i 1 ri 1 is a tuning parameter such that the N Let of user i under policy Q where 1{.} is the indicator smaller the value of , the less restrictive the function. We have fairness constraint, and the greater the opportunity to improve the system performance. T (Q) i 1 Ti (Q) E (U Q (U ) ). N * An optimal policy Q is defined as follows: Of course, the values of Ti (Q ) depends on the Q* (U ) arg maxi (ui* Ui ) , distribution of U , which is ignored in the notation * for simplicity. In this section, we summarize some where the u i s are real parameters satisfying results in opportunistic scheduling. It is interesting a) mi n i (ui ) 0 ; that optimal policies turn out to be simple, easily * implementable index policies under various fairness and QoS constraints. b) for all i, P{Q* (U ) i} ri . We should note that the problem formulations are c) for all i, if P{Q (U ) i} ri then u i =0. * * expressed in terms of expectation, which is a long- term performance measure. Short-term fairness * Let us explain the heuristics of the policy Q , which depends on the time-correlation of the performance values and can be tuned through parameter is helpful to understand the intuition of opportunistic * estimations. It will be discussed in Section 4.2. scheduling. For a proof of the optimality of Q , we 3.1. Temporal Fairness refer readers to [11]. We can think of the parameter u i* above as an ―offset‖ used to satisfy the fairness Because time is the resource shared among users, a natural fairness criterion is to give each user at least a requirement. To elaborate, consider the case where we want to maximize the overall performance certain share of the entire resource, i.e., time. Let ri without any QoS requirements. It is straightforward denote the minimum time-fraction that should be to show that we should always choose the ―best‖ user N assigned to user i, where ri 0 , r 1 , and i 1 i (i.e., the user with the maximum performance value) N is the number of users in the cell. Here, we assume to transmit. In other words, Q* (U ) arg maxi Ui . However, such a scheme may be unfair to certain that the ri s are predetermined and serve as pre- users. Hence, to satisfy the fairness requirement, the specified fairness constraints. The value of ri scheduling policy schedules the ―relatively-best‖ user to transmit. User i is ―relatively-best‖ if dictates the minimum fraction of time that a user should transmit on the channel, which is typically ui* Ui u* U j for all j. If u i* >0, then user i j determined by the user's class, the price the user is is an ―unfortunate‖ user, i.e., the channel condition it willing to pay for the wireless service, or the user's experiences is relatively poor. Hence, it has to take current channel conditions. The scheduling advantage of some other users (e.g., users with algorithm then decides which time-slot should be assigned to which user, given the minimum time- u *j =0) to satisfy its fairness requirement. Thus, to fraction requirement. Our goal is to develop a maximize the overall system performance, we can scheduling policy Q that exploits the time-varying only give the ―unfortunate‖ users the amount of resource equivalent to their minimum requirements. channel conditions to maximize the total expected system performance while satisfying the resource- Last, when P{Q* (U ) i} ri for user i, the user sharing constraint. The problem can be stated gets more than its minimum requirement---this user formally as follows: * cannot take advantage of other users, i.e., u i =0. In max Q E(U Q(U ) ) summary, condition (a) above on u i* is for normalization and condition (b) is the feasibility subject to P{Q(U ) i} ri , i 1,2,...N requirement. Condition (c) is important to the * In words, the problem is to find an optimal policy optimality of Q . Its heuristic interpretation is that a among all policies such that the total system good user that gets more than its minimum throughput is maximized where each user’s resource- requirement cannot take advantage of other users. sharing requirement is satisfied. Note that This condition can also be explained in terms of complementary slackness: if the constraint is not b 1 i 1 ai vi* , and the v i* s are real N where active (i.e., the average performance of user i is greater than its minimum requirement), then the parameters satisfying * corresponding u a) mi n i ( vi ) 0 ; (which can be interpreted as a * i Lagrange multiplier) is zero. In a special case where b) for all i, Ti (Q ) ai T (Q ); * * users have independent and identically distributed c) for all i, if Ti (Q ) ai T (Q ); then v i =0. performance values and the same requirements, we * * * have ui* u * and Ti (Q* ) T j (Q* ) for all i and j. j The authors of [9] consider a special case of the above opportunistic scheduling problem. Property: If the performance values U i s, Specifically, they consider maximizing the minimum i 1,2,...N , are independent, then weighted performance of users. This is a special case of the utilitarian fairness problem defined in this Ti {Q} P{Q(U ) i}U i riU i , i 1,2,...N. section. This problem setting requires fairness in terms of This property makes a strong statement about the performance values, which, to some extent, parallels individual performance of each user. If users’ the concept of weighted fair queueing used in performance values are independent, the average wireline networks. The difference is that the overall performance of every user in our opportunistic capacity here is not fixed; it depends on channel scheduling scheme will be at least that of any non- opportunistic scheduling scheme. In this sense, the conditions, the values of a i , and the scheduling opportunistic scheduling policy does not sacrifice any policy. user’s performance to improve the overall system * performance. Of course, different users may The parameter v i can be considered a ―scaling‖ used experience different amounts of improvement. This to satisfy the utilitarian fairness constraint. The property can also be explored to provide direct optimal scheduling policy always chooses the performance guarantees to users with simple resource relatively-best user to transmit. In this case, a user is allocation schemes. relatively-best if (b v* )U j arg maxi (b vi* )Ui . * The values of the u i s are determined by the j distribution of U and the values of the ri . In * As before, if v i >0, then the user is an ―unfortunate‖ practice, the distribution of U is unknown, and user, and its average performance value equals the * minimum requirement. hence we need to estimate the parameter u i . Similarly, in the opportunistic scheduling schemes Utilitarian scheduling schemes have certain notable discussed in other sections, there are also parameters features. First, the utilitarian fairness constraint that need to be estimated. Estimations of the controls the maximum discrepancy of performance parameters are discussed in Section 3.5. values among users. Second, the constraint given ensures that a user is given at least a certain share of 3.2. Utilitarian Fairness the total performance, and is hence more suitable in The problem formulation of the utilitarian fairness is some situations than the temporal fairness constraint. presented as However, there is also a significant disadvantage of a utilitarian scheduling scheme: a user experiencing max Q T (Q ) poor channel conditions could have a detrimental impact on the overall system performance because a subject to Ti (Q) aiT (Q), i 1,2,... N , substantial portion of the total time-slots may have to be allocated to this user in order to meet its fairness N where ai 0, and ai 1. requirement. To alleviate this potential problem, one i 1 can devise an adaptive threshold strategy [11]. An optimal policy is defined as follows: 3.3 Minimum-performance Guarantee Q* (U ) arg maxi (b vi* )Ui Thus far, we have discussed two optimal scheduling schemes that provide users with different fairness guarantees. From a user’s viewpoint, a more direct QoS is defined in terms of minimum-performance guarantees. To elaborate, the objective is to always provides ―no-worse‖ performance values for maximize the average system performance subject to each user relative to that of the non-opportunistic meeting each user's minimum-performance scheduling policy, assuming that the signaling cost is requirement, formulated as: negligible. Thus, the opportunistic scheduling policy dominates non-opportunistic policies. max Q T (Q ) 3.4 Index Policies subject to Ti (Q) Ci , i 1,2,... N It turns out that a scheduling policy of the form of where C i is the minimum-throughput requirement of Q* (U ) arg maxi i*Ui user i. Consideration of this problem raises two is optimal for many types of scheduling problems. questions: (i) Is the requirements feasible, i.e., does For example, the optimal utilitarian policy defined there exist a policy such that Ti (Q ) Ci , for all i? earlier is in this form. If i* 1 for all i , then the (ii) If it is feasible, which policy maximizes the policy maximizes the total system throughput. On the overall performance under the given QoS requirement? other hand, if i* 1 / Ti (Q * ) for all i , then the Compared to fairness requirements, the formulation policy is proportional fair [2]. here offers users a more ―direct‖ service guarantee. In [5,6], the authors study scheduling algorithms For example, if the performance measure is defined where both delay and channel conditions are taken as the data-rate, then each user is guaranteed a into account. Roughly speaking, the algorithm is: minimum data-rate, which may be more important to a user than knowing that a minimum amount of Q* (U ) arg maxi i*UiWi , resource will be assigned to it. While appealing to users, providing minimum-performance guarantees where Wi is the head-of-the-line packet delay for can be quite difficult in practice because of the feasibility issue---can the system satisfy the queue i, and i* is some constant. The policy is performance requirements for all users? (Note that throughput optimal. feasibility is not a concern in the fairness-based constraints.) More discussion on feasibility can be We have presented a framework for opportunistic found in [11]. There are, however, some natural scheduling and studied different scheduling settings where feasibility is not a problem. For problems. These scheduling problems share a example, the requirements can be set as the average common goal: to improve the spectrum efficiency data rates in a non-opportunistic round-robin while maintaining certain levels of QoS for each user scheduling scheme. Then, it is guaranteed to be using opportunistic scheduling algorithms. The feasible for opportunistic scheduling policies. solutions to these scheduling problems turn out to be index policies---all the schemes choose the An optimal policy is defined as follows: ―relatively-best‖ user to transmit. Although ―relatively-best‖ has a different meaning for each Q* (U ) arg maxi i*Ui scheduling policy, the basic idea is to use an offset or a scaling to satisfy the QoS requirements for users. In where i* s are real parameters satisfying general, the larger the number of users sharing the a) mi n i ( ) 1 ; * same channel, or the larger the variance of U , the i larger the ―opportunistic‖ scheduling gain compared b) for all i, Ti (Q ) Ci ; * with non-opportunistic scheduling policies. Furthermore, the more restrictive the QoS constraint, c) for all i, if Ti (Q ) Ci , then * i* =0. the less the flexibility for opportunistic scheduling decisions, and the lower the system performance The parameter i* ―scales‖ the performance values gain. of users, and the scheduling policy schedules the relatively-best user, where a user is relatively-best if 3.5 Implementation *U j arg maxi i*Ui . If the scaling factor for a j Figure 1 shows a block diagram of a practical scheduling procedure that incorporates on-line user is larger than 1, then the user is an ―unfortunate‖ parameters estimation. In our scheduling policy, the user, and it is granted only an average performance base station needs to obtain information of each value that equals its minimum-performance user’s performance value at a given time slot to make requirement. The opportunistic scheduling policy the scheduling decision. At a time slot, a user could gik (uik min j u k )(1{Qk (U ) i} ri ) , j measure the received signal power level (from the user’s base station) and the interference power level. where i=1,2,…N. The observation error in this case is Based on the estimated SINR, the user can then obtain its performance value. The information is sent eik g ik f i (u k ) back to the base station, which can be accomplished in several ways. For example, each user could (uik min j u k )(1{Q k (U ) i} P{Q k (U ) i}) j maintain a small signaling channel with the base station. Such signaling/control channels have been standardized in the third generation cellular networks. which is an unbiased estimate. Hence, we can use a Then the base station makes the scheduling decision stochastic approximation algorithm of the form based on the scheduling policy and transmits to the selected user. Last, parameters used in the scheduling uik 1 uik k g ik , policy are updated, which is discussed next. where, e.g., k =1/k. When uik min j u k , we also need to ensure that j P{Q (U ) i} ri . If P{Q k (U ) i} ri , then k u k is an infeasible parameter vector, which causes Figure 1. Block diagram of the scheduling policy some fairness constraint to be violated. To ensure k with on-line parameter estimation. that u converges to u * , we should project u k The opportunistic scheduling policies described in u s. However, because we do onto the feasible set of previous sections all involve some parameters that not have knowledge of the distribution of U , it is need to be estimated online. Such parameters are very difficult to find the exact projection. Hence, we determined by the values of the QoS requirements use the following intuitive algorithm as a projection. and the distribution of the utility values. In practice, such a distribution is a priori unknown, and hence we It is easy to see that P{Q (U ) i} is an increasing k need to estimate the parameters. In this section, we use the temporal fairness scheduling scheme as an k function of u i . Hence, if uik min j u k , and j example to describe briefly how to estimate these parameters efficiently via stochastic approximation P{Q k (U ) i} ri , then we increase the value of techniques. Similar estimations can be applied for u ik to increase the value of P{Q k (U ) i} , as a other scheduling policies. projection to the feasible set. Although we do not Recall that the parameters are chosen to satisfy the know the value of P{Q (U ) i} , we can estimate k following requirement: for all i, if k P{Q(U ) i} ri then u i* =0. Hence, we can write it by a moving average. Let p i be the estimate of as a root of the equation f (u ) 0 , where the ith P{Q k (U ) i} . We update pik in each time-slot component is given by as follows: fi (u ) (ui min j u j )(P{Q(U ) i} ri ) , pik (1 w) pik 1 w1{Qk (U ) i}, where i=1,2,…N. Next, we use a stochastic where w is a constant, indicating how fast p i tracks k approximation algorithm to generate a sequence of P{Q k (U ) i} . If pi ri , k iterates u 1 , u 2 , u 3 , … that represent estimates of and u * . Each u k defines a policy Q k given by u min j u , then we increase the value of u by k i k j k i k Q k (U ) arg maxi (Ui uik ) . To construct the a small constant. By doing this, we push u towards stochastic approximation algorithm, we need an the feasible set of u s. Simulations indicate that this estimate of f (u k ) . Although we cannot obtain approach works well. f (u k ) directly, we have a noisy observation of its 4. Discussion components: Different schemes may be suitable for different scenarios. For example, if the service provider wants to build a simple wireless network with pricing, the Opportunistic scheduling exploits the fluctuation of temporal fairness scheduling scheme is a reasonable channel conditions, and thus scheduling gain choice. The temporal fairness scheduling scheme is inherently depends on the amplitude of the variations simple and flexible without feasibility concerns. The of channels. In general, the greater the fluctuation of amount of resource consumed by a user determines channel conditions, the larger the number of users, the minimum performance the user gets (with the better the performance gain. technical assumptions). The resource consumed by a Another concern in opportunistic scheduling is the user can be connected directly with the price the user time scale of fluctuation. The fluctuation of channels should pay. On the other hand, the minimum- should be slow enough for users to estimate and performance guarantee scheme provides users a exploit it. On the other hand, the fluctuation should direct performance assurance, but involves the be fast enough, so that users won’t experience additional complication of feasibility. If the service extreme long delays. Though many data users are provider wants to build a network that provides data- delay-tolerant, extreme delays may cause upper-layer rate guarantees, then this scheme is an appropriate problems such as TCP timeout. choice. However, in practice, the feasibility issue may be difficult to handle, especially in a wireless There is a tradeoff between scheduling gain and setting, and providing service performance short-term performance. In general, the stronger the guarantees is challenging in both wireless and time-correlation of channel conditions (i.e., the wireline networks. slower the channel fluctuation), the worse the short- term performance, and the greater the improvement It should be noted that the framework for in the short-term performance, the less the scheduling opportunistic scheduling that we have described here gain. can also cover cases where there are different constraints from different users. For example, some In general, scheduling gain increases as the number users may have resource requirements while other of users increases. However, the normalized users can have a minimum-data-rate requirement. In scheduling gain (scheduling gain over number of such scenarios, similar optimal solutions can be users) decreases with the increase of the number of provided under this framework using similar users, while the signaling cost per user remains the optimization techniques. same. Hence, it is a question of practical importance to decide the number of users sharing the same 4.1 Precautionary Notes channel. Opportunistic scheduling schemes, as an illustration In summary, opportunistic scheduling presents a new of the cross-layer design of wireless systems, exploit design approach, especially for delay-tolerant data time-varying channel conditions of users with the traffic. It has its own advantages and limitations. It is objective to improve the system throughput. thus important that the system designer to take a However, nothing comes for free. Opportunistic holistic view of the cross-layer design in order to scheduling also has its own costs and limitations avoid potential negative system-wide impacts. discussed as follows. 4.2 Possible Research Directions There are signaling costs involved in all opportunistic scheduling schemes because scheduling decisions Many interesting problems are yet to be resolved in inherently depend on channel. Users need to opportunistic scheduling. We discuss some possible constantly estimate their channel conditions and research problems next. report to the base station. Hence, the actual Short-term Fairness As mentioned earlier, the scheduling gain should take into account the scheduling problems are expressed in terms of signaling costs. expectation in this paper, which is a long-term Because users need to estimate the channel performance measure. There is no guarantee of short- conditions, estimation errors occur in all scheduling term performance. In [10], an extension is provided schemes. There are various sources of estimation to improve short-term performance. The basic idea is errors: errors of estimations of channels, errors of to increase a user's probability of transmission when estimations of parameters involved in scheduling it is behind in its share. There is a need for general schemes, and errors caused by various delays such as short-term fairness criteria tailored to wireless transmission delay, estimation delay, and restriction networks and dealing with the short-term of time-slots, etc. In general, if the variation of performance in depth. We also refer interested channel conditions is relatively slow, then the readers to [5-8] where queueing delays are estimation is good. We recommend a rigorous study considered, [13] where real-time scheduling is on this problem, especially in the case of fast fading. discussed, and [27] where user-level performance is studied. layer-breaking designs can be potentially beneficial. Delay A problem related to improving short-term Admission Control The opportunistic scheduling performance is to schedule traffic with deadlines, i.e., problems studied here have the net effect of increas- real-time traffic. Specifically, upon arrival, each real- ing the overall effective capacity of the wireless time packet has a delay deadline, and packets that network. This means that the network can now cannot be transmitted before their deadlines are accommodate more users or higher-data-rate users. dropped/marked. Research on scheduling with Thus, we know that keeping all else fixed, the deadlines in the wireline setting has led to various admissible region of the wireless network will approaches. The additional challenge in wireless increase by using opportunistic scheduling schemes. networks is due to the time-varying channel A challenging problem that still remains is how to conditions. Approaches to these problems may make intelligent admission control decisions on include off-line optimal solutions with the whether or not to allow a new user into a cell. assumption of entire traffic and channel information, Although admission control is a difficult problem in on-line model-based solutions, and heuristic/greedy wireless systems whether or not opportunistic algorithms. Heuristic algorithms play an important scheduling is used, it is more challenging in the role in real-time scheduling problems because context of opportunistic scheduling because (typically) the optimal scheduling problem is NP- opportunistic scheduling increases the system complete and simplicity is a desirable feature. In the dynamics. wireline world, it is sometimes the case that Multi-hop Networks Most of the current research on complicated scheduling schemes do not have opportunistic scheduling focuses on the downlink of significant performance gains over simple schemes, a cellular system. In such a system, there exists a such as static priority or earliest-deadline-first. A natural central controller, the base station. An similar situation may be expected to hold for wireless interesting question is whether and how to exploit the networks. time-domain diversity in a distributed multi-hop Another challenging problem is to minimize the environment, such as an ad-hoc network average packet delay. Although many schemes can [15,20,24,28]. stabilize the queues, to control the average delay 5. Conclusion performance is much more challenging. To meet the increasing demand for wireless services, Multi-carrier System Opportunistic scheduling is especially affordable wireless data services, wireless based on the premise that the wireless channel is spectrum efficiency is becoming increasingly im- time-varying, and we can schedule users to transmit portant. In wireless networks, users experience at those times that are opportunistically ―relatively unreliable, location-dependent, and time-varying good.‖ This idea can be extended to the frequency channel conditions. Traditionally, the channel domain: we opportunistically schedule users to variation is considered as a negative factor for frequencies (and time) that are relatively good [19]. reliable communication, and should be mitigated by An example of such systems is an OFDM system. A methods such as time interleaving, power control, concern of opportunistic scheduling in such systems and multiple antennas. On the other hand, is the signaling cost. Because each sub-carrier is very opportunistic scheduling is designed to exploit the narrow in OFDM systems, signaling should be variation of channel conditions to improve spectrum carefully designed to ensure good channel estimation efficiency. It adds an additional degree of freedom to of users on different sub-carriers while avoiding the system: time-domain diversity or also called significant signaling overhead. multi-user diversity. It improves spectrum efficiency, Physical Layer The performance of opportunistic especially for delay-tolerant data transmissions. scheduling schemes is closely related to physical- Various opportunistic scheduling schemes have been layer designs. As explained earlier, estimation errors studied. A common objective is to improve/maximize occur in all opportunistic scheduling schemes. On system performance (e.g., throughput) under various one hand, we need a better understanding of the fairness and QoS constraints. In many cases, the effect of channel estimation errors on scheduling optimal policies are given in a simple parametric schemes. On the other hand, it calls for better channel form, hence lending themselves to easy estimation techniques and smart coding schemes implementations. The advantages of opportunistic (e.g., incremental redundancy transmission schemes scheduling also include the ability to work with other with turbo codes). Further, it is also important to resource management mechanisms. A good example study the performance of opportunistic scheduling in of this is the joint scheduling and power-allocation multiple antenna systems. In summary, a better scheme [23]. In summary, opportunistic scheduling, understanding of physical-layer technologies or even with its own advantages and limitations, is an excellent illustration of cross-layer design. [15] X. Qin and R. Berry, ―Exploiting multiuser diversity for medium access control in wireless networks,‖ in 6. Acknowledgement Proceedings of IEEE Infocom 2003. IEEE, 2003. This research is supported in part by NSF awards [16] ——, ―A distributed splitting algorithm for exploiting ANI-0207728, ANI-0099137, EIA-0130599, ECS- multiuser diversity,‖ in Proceedings of IEEE International 0098089 and ANI-0207892, and the Indiana 21st Symposium on Information Theory. IEEE, 2003. century center for wireless communications and [17] B. M. Hochwald, T. L. Marzetta, and V. Tarokh, networking. ―Multiple-antenna channel hardening and its implications 7. References for rate feedback and scheduling,‖ IEEE Transactions on Information Theory, vol. 50, no. 9, pp. 1893 – 1909, Sept [1] Y. Cao and V. Li, ―Scheduling algorithms in broadband 2004. wireless networks,‖ Proceedings of the IEEE, vol. 89, no. 1, pp. 76–87, January 2001. [18] S. Borst and P. Whiting, ―The use of diversity antennas in high-speed wireless systems: Capacity gains, [2] P. Bender, P. Black, M. Grob, R. Padovani, N. fairness issues, multi-user scheduling,‖ Bell Laboratories Sindhushyana, and A. Viterbi, ―CDMA/HDR: a bandwidth- Technical Memorandum, 2001. efficient high-speed wireless data service for nomadic users,‖ IEEE Communications Magazine, vol. 38, no. 7, pp. [19] Y. Liu and E. Knightly, ―Opportunistic fair scheduling 70–77, July 2000. over multiple wireless channels,‖ in Proceedings of IEEE INFOCOM 2003, 2003. [3] A. Jalali, R. Padovani, and R. Pankaj, ―Data throughput [20] Q. Zhao and L. Tong, ―Distributed opportunistic of CDMA-HDR a high efficiency-high data rate personal transmission for wireless sensor networks,‖ in 2005 IEEE communication wireless system,‖ in Proceedings of IEEE International Conference on Speech, Acoustics, and Signal Vehicular Technology Conference 2000-Spring, vol. 3, Processing. 2000. [21] J. W. Lee, R. R. Mazumdar, and N. B. Shroﬀ, [4] F. 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