Managing Waiting Lines chapter - 13 by noBt8t

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									Managing Waiting Lines
    chapter - 13

                Learning Objectives
 Describe   how queues form.
 Apply Maister's two “laws of service.”
 Discuss the psychology of waiting.

 Describe the essential features of a queuing system.
 Explain the equivalence of Poisson arrival rates and
  exponential time between arrivals.

                   Queuing Systems
A     queue is a line of waiting customers who require service
    from one or more servers.
 The    queue need not be a physical line of individuals in front
    of a server, example, being placed on hold by telephone
 Servers  typically are considered to be individual stations
    where customers receive service.
    In any service system, a queue forms whenever current
    demand exceeds the existing capacity to serve. Such a
    situation is bound to occur in any system for which arrivals
    occur at varying times and service times also vary.

   Different kinds of queuing systems
 Serversneed not be limited to serving one customer at a
 time. Example, transportation system such as buses,
 airplanes, and elevators are bulk services.

 The consumer need not always travel to the service facility;
 the server actually may come to the consumer, example,
 police protection, ambulance service.

 Theservice may consist of stages of queues in a series or of
 a more complex network of queues. Example, Disneyland,
 where queues are staged in sequence.

                  Waiting Realities
 Inevitabilityof Waiting: Waiting results from variations in
 arrival rates and service rates

 Economics   of Waiting: High utilization purchased at the
 price of customer waiting. Example, doctor’s clinic.

            The Psychology of Waiting
 Maister’s   two laws of service
   First law deals with the customer’s expectation versus
    perceptions. If customer’s receive better service than he or she
    expects, then the customer departs a happy, satisfied person.
    He/she will then tell his friends the positive experience; but he/she
    will also share the bad experience and hurt the service.

   Second    law states that it is hard to play ‘catch-up-ball’. The first
    impressions formed during wit time may impact perceptions for
    rest of the service. Therefore, customer wait time should be
    managed well.

                The Old Empty Feeling
 People    dislike waiting time, because it seems
   Uncomfortable
   Insulting
   Powerless
   Lasts   forever

 Sofill the wait time with positive ways to keep customers
   Mirrors
   Furnishings  and music
   T.V., reading material
   Coffee and cookies
   Live entertainment

                    A Foot in the Door
 Convey to the customer that the service has begun, because
 they can tolerate the wait much longer than if service has not
 even started, example,
   Handing   them menus while they are waiting in the line

   Asking   them to fill in their medical history

       The Light at the End of the Tunnel
 Anxiety  of waiting in a line with unknown wait time is not
  good. Therefore, telling the customer how long the wait time
  will be allows the customer to decide whether to wait or not.

   the customer has to wait then a simple explanation and
 If
  apology for the delay will go a long way in establishing

           Excuse me, but I was next
 FCFS   should be the primary rule used for service.

 Use  ticketing system to determine the priority instead of
  physical line. The number being served can be displayed so
  that customer will know how long the wait time will be.

 Itwill also allow customers to wander around and may do
  some impulse buying.

 Such a system will also work well if there are multiple

             The Economics of Waiting
         customer when kept waiting in line for service or
 Internal
 product – means unproductivity and lost wages.
 External   customer when kept waiting may mean lost sales
 Strategy   to avoid lost sale
   Conceal  the queue from arriving customers, ex., in a hotel divert
    the customers to the bar so that people cannot be seen as waiting

   Disney  charges customers outside the park where customers
    cannot see the lines. Inside, they design the lines in such a way
    that you cannot see many customers waiting before you.

   Design  the service to involve the customers to participate in
    service delivery during wait, ex, filling medical history

   Use  wait time to educate customers about your new product and

       Essential Features of Queuing Systems


             Arrival                    Queue
             process                                          Departure
Calling                   Queue        discipline   Service
population             configuration                process
             Balk                                                    No future
                                                                     need for

                      Calling population
 Calling    population is the arrival or input to the system
 Itmay not be homogenous; it may consist of several
    Example,     arrivals at an outpatient clinic can be divided into walk-in
       patients, patients with appointments, and emergency patients

    Each    class of patients has different needs from the service
       provider and also their waiting expectations are different

 Insome queuing systems, the source of calls may be limited
 to a finite number of people.
   Example,     demands on an office copier by a staff of 3 secretaries

   Here,     the probability of future arrivals depends on the number of
       persons who are in the system seeking service. Example, the
       probability of a future arrival becomes zero once the 3rd secretary
       joins the copier queue.

             Arrival Characteristics
 Size of the population
 Pattern of arrivals in the queuing system
 Behavior of the arrivals

                Size of population
 Unlessthe population is quite small, an assumption of
 independent arrivals or infinite population usually suffices.
 When  the number of customers or arrivals on hand at any
 given moment is just a small portion of potential arrivals, the
 calling population is considered unlimited.
 Mostqueuing models assume such an infinite calling

                   Arrival Process
 The rate at which the customers arrive is determined by the
 arrival process.
        of arrival can be deterministic or random. Typically,
 Pattern
 we assume random arrival process.
 Dataare collected by recording the actual times of arrivals,
 which are then used to calculate inter-arrival times.
        show that the distribution of inter-arrival times will be
 Studies
 an exponential distribution (see figure 13.3). It has a high
 frequency at the origin and the long tail that tapers off to the
 The mean and the standard deviation of exponential
 distribution are theoretically equal)

The exponential distribution has a continuous probability
 density function of the form

                   f(t) = λe-λt           t≥0
λ = average arrival rate within a given interval of time (e.g.
  minutes, hours, days). On average how many arrive within a
  specified time period.
t = time between arrivals
μ = 1/λ (mean time between arrivals)
e = base of natural logarithms (2.718)

                          F(t) = 1 – e-λt
Cumulative distribution function, which tells us the probability
 that the time between arrivals will be time period t or less.

What is the probability that a patient will show up in the next 5
  minutes; given that the mean time between arrivals is 2.4
μ = 2.4 , therefore , λ = 1/2.4 = 0.4167 arrivals per minute
F(5) = 1 – e-0.4167(5)
 = 1 – 0.124
 = 0.876 = 87.6%

                Poisson Distribution
The number of arrivals can be estimated by Poisson
 distribution. It tells us the probability of n arrivals during the
 time interval t (usually t = 1).

                          P(n) = (λt)ne-λt

λ = average arrival rate within a given interval of time (e.g.
  minutes, hours, days)
n = number of arrivals
t = number of time periods of interest (usually t = 1)
e = base of natural logarithms (2.718)

 What is the probability that 2 patients will show up in the
 next 1 hour; given that the mean time between arrivals is 2.4

μ = 2.4 , therefore , λ = 1/2.4 = 0.4167 arrivals per minute
Arrivals in 1 hour, λt = 0.4167 x 60 minutes = 25 arrivals per hr

P(2) = (25)2 e-25 = 625 x (2.7183)-25
           2!              2x1
Probability that no patient will arrive during 1 hour interval
P(0) = (25)0 e-25 = (2.7183)-25

          Poisson and Exponential Equivalence

Poisson distribution for number of arrivals per hour (top view)
  1          2          0         1         interval
Arrival   Arrivals   Arrivals     Arrival

62 min.
             40 min.
                                123 min.

Exponential distribution of time between arrivals in minutes (bottom view)

              Behavior of the arrivals
 Mostqueuing models assume that an arriving customer is a
 patient customer, they will wait in the Queue until they are
 served; and they do not switch between lines.
 The  demand rate during the unit of time should be stationary
 with respect to time, i.e lambda is a constant; otherwise, the
 underlying fluctuations in demand rate as a function of time
 will not be accounted for. This dynamic feature of demand is
 illustrated in fig. 13.5 for hours in a day; fig. 13.6 for days of
 a week; and fig. 13.7 for months of the year.
 Variationin demand intensity directly affects the
 requirements for service capacity. When possible, service
 capacity is adjusted to match changes in demand, perhaps
 by varying the staffing levels.

                         Temporal Variation in Arrival Rates

                                                                Percentage of average daily
                         3.5                                                                  140
Average calls per hour

                           3                                                                  130

                                                                      physician visits
                         2.5                                                                  120
                           2                                                                  110
                         0.5                                                                   70
                           0                                                                   60
                               1 3 5 7 9 11 13 15 17 19 21 23                                       1   2        3        4   5
                                         Hour of day                                                        Day of week

               Queue configuration
 Queue   configuration refers to the number of queues, their
  locations, their space requirements, and their effects on
  customer behavior.
 Balking refers to customers who arrive but refuse to join the
  waiting line because it is too long to suit their needs or
 Reneging customers are those who enter the queue but
  then become impatient and leave without completing their
 Jockeying is the line switching activity; when the customer
  finds another line moving faster than his/her and they switch.

A  queue can be limited or unlimited. A queue is limited when
 it cannot by law or by physical restrictions increase to an
 infinite length ( example, space in a bank may limit the
 queue to 10 customers)
 Rules that maybe used to serve the arriving customers;
 typically we use the FCFS
 Number  of service channels or number of servers, that is
 single versus multiple
 Number of phases or number of service stops that must be
 made, single versus multiple

        Queue Configurations (fig. 13. 9)

    Multiple Queue                Single queue

    Take a Number
3       4                  2

    8   6         10
                 12        7
            11         9

 Multiple   queue alternative (fig. 13.9a)
   The arriving customer must decide which queue to join. Of course
    they can switch

   Service provided can be differentiated to attend to different needs;
    ex. Fast lane for shorter orders

   Division  of labor is possible, allowing different servers to do
    different things

   Customers    have a choice to select the server they prefer

   Balkingbehavior is deterred because lines look smaller than if
    there was only one line

 Single   queue (figure 13.9b)
   The    first person in the line moves to the available service counter

   Reneging   becomes difficult because customer finds hard to leave
    the line once more customers gather behind

   The    arrangement ensures fairness, that is, FCFS rule is applied

   There  is a single line; thus no anxiety is associated with waiting to
    see if another line is moving faster

   Privacyis enhanced because the transaction is conducted with no
    one standing immediately behind the person being served

   Thisarrangement is more efficient in terms of reducing the
    average time that customers spend waiting in line

 Variation    of single queue system (figure 13.9c)
   Arriving   customer takes a number to indicate his or her place in
    the line

   There   is no need for a formal line; customers can wander around
    but remain alert to hear their number being called or risk missing
    their turn for service

 Virtual   queue
   On  phone, when it is hard to determine how long is the wait time;
    but now, they can calculate the average wait time per customer
    and then the order in which you call they can inform you of the
    wait time.

                       Queue Discipline


      (FCFS rule)

        selection                            Selection based
     based on status                          on individual
        of queue                                customer

Number of                                                      Processing time
customers     Round robin         Priority     Preemptive       of customers
 waiting                                                          (SPT rule)

                  Queue Discipline
 Itis the policy established by management to select the next
  customer from the queue for service.
 Most  popular is the FCFS rule; which is static because no
  information other than position in line is used to identify the
  next customer for service. So the customers are served in
  the order they arrive.
 Dynamic    queue disciplines are based on some attributes of
  the customer or status of the waiting line. For example,
  shortest processing time rule will change the order of
  service of the customer to minimize the average time the
  customer spends in the system. There are number of other
  similar rules used to change the dynamic ordering of

   medical setting, they use the procedure known as triage,
 In
 which gives priority to those who would benefit most from
 immediate treatment.
 Preemptive  – here the service currently in process for a
 person is interrupted to serve a newly arrived customer with
 higher service urgency; example, what we see in medical
         – when the importance of customer decides the
 Priority
 order of their service; example, an important customer may
 not stand in a line but be served personally by the manger.

    Number of customers waiting – as a policy measure the
    organization may open more check out counters once they
    see more than a certain number of customers in a line. They
    may also start taking orders from customers in line
 Round    robin – is used by time shared computer systems,
    where a customer is given partial service, and then the
    server moves on to the next waiting customer. Thus
    customers alternate between waiting and being served.
 The     queue discipline can have an important effect on the
    likelihood that a waiting customer will renege – because the
    rule used to serve will impact the wait time for a customer.

                  Service Process
 Thedistribution of service times, arrangement of servers,
 management policies, and server behavior all contribute to
 service performance.
 Servicetime can be a constant, such as the time to wash a
 car through an automated car wash.
           the service time is not a constant, example,
 Typically,
 serving at a fast food window, collecting toll at a bridge –
 here the service time frequently is exponential distribution.
 The distribution of service times is a reflection of the
 variation in customer needs and server performances.

          Service facility arrangement
         servers – provides flexibility in meeting variation in
 Parallel
 demand for service. Management can vary the service
 capacity by opening and closing service lines to meet
 changes in demand.
 Cross   training is important for parallel service
 Behaviorof service providers is important for success.
 Under pressure, if provider speeds up, then some customers
 may interpret as bad quality.

          Service Facility Arrangements
                   (table 13.1)
Service facility                         Server arrangement
 Parking lot       Self-serve

 Cafeteria         Servers in series

 Toll booths       Servers in parallel

 Supermarket       Self-serve, first stage; parallel servers, second stage

 Hospital          Many service centers in parallel and series, not all used by each patient

                 Arrival Process (fig. 13.8)


             Static                                  Dynamic

   Random         Random arrival                               Customer-
                                       Facility-               exercised
 arrivals with     rate varying
                                      controlled                control
constant rate        with time

Accept/Reject         Price         Appointments   Reneging     Balking

         Approaches to Controlling Customer Waiting

 Animate:   Disneyland distractions, elevator mirror, recorded
 Discriminate:   Avis frequent renter treatment (out of sight)
 Automate:    Use computer scripts to address 75% of
 Obfuscate:   Disneyland staged waits (e.g. House of

               The Art of Service Recovery
               “To err is human; to recover, divine”
 Measure      Cost of Lost Customer
 Listen   Carefully
 Anticipate    Need for Recovery
 Act   Fast
 Train   Employees
 Empower       the Frontline
 Inform   Customers of Improvement

               Topics for Discussion
 Suggest   some strategies for controlling variability in service
 Suggest  diversions that could make waiting less painful.
 Select a bad and good waiting experience, and contrast the
  situations with respect to the aesthetics of the surroundings,
  diversions, people waiting, and attitude of servers.
 Suggest ways that management can influence the arrival
  times of customers.
 What are the benefits of a fast-food employee taking your
  order while waiting in line?

             Interactive Exercise
The class breaks into small groups with at least one
international student in each group, if possible. Based on
overseas travel, each group reports on observations of
waiting behavior from a cultural perspective.

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