Managing Waiting Lines chapter - 13

1. Managing Waiting Lineschapter - 13

2. 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.

3. 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 operator. • 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.

4. Different kinds of queuing systems • Servers need 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. • The service 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.

5. Waiting Realities • Inevitability of 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.

6. 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.

7. The Old Empty Feeling • People dislike waiting time, because it seems • Uncomfortable • Insulting • Powerless • Lasts forever • So fill the wait time with positive ways to keep customers busy • Mirrors • Furnishings and music • T.V., reading material • Coffee and cookies • Live entertainment

8. 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

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

10. 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. • It will also allow customers to wander around and may do some impulse buying. • Such a system will also work well if there are multiple servers

11. The Economics of Waiting • Internal customer when kept waiting in line for service or 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 services

12. Renege Arrival process Queue discipline Departure Calling population Service process Queue configuration No future need for service Balk Essential Features of Queuing Systems

13. Calling population • Calling population is the arrival or input to the system • It may not be homogenous; it may consist of several subpopulations. • 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

14. continued • In some 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.

15. Arrival Characteristics • Size of the population • Pattern of arrivals in the queuing system • Behavior of the arrivals

16. Size of population • Unless the 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. • Most queuing models assume such an infinite calling population.

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

18. continued 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)

19. continued 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 minutes. μ = 2.4 , therefore , λ = 1/2.4 = 0.4167 arrivals per minute t = 5 F(5) = 1 – e-0.4167(5) = 1 – 0.124 = 0.876 = 87.6%

20. 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 n! 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)

21. continued • 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 minutes. 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! 2 x 1 Probability that no patient will arrive during 1 hour interval P(0) = (25)0 e-25 = (2.7183)-25 0!

22. Poisson and Exponential Equivalence Poisson distribution for number of arrivals per hour (top view) One-hour 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)

23. Behavior of the arrivals • Most queuing 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. • Variation in 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.

24. Temporal Variation in Arrival Rates

25. 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 interests. • Reneging customers are those who enter the queue but then become impatient and leave without completing their transaction. • Jockeying is the line switching activity; when the customer finds another line moving faster than his/her and they switch.

26. continued • 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

27. Queue Configurations (fig. 13. 9) Multiple Queue Single queue Take a Number Enter 3 4 2 8 6 10 12 7 11 9 5

28. continued • 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 • Balking behavior is deterred because lines look smaller than if there was only one line

29. continued • 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 • Privacy is enhanced because the transaction is conducted with no one standing immediately behind the person being served • This arrangement is more efficient in terms of reducing the average time that customers spend waiting in line

30. continued • 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.

31. Queue discipline Static (FCFS rule) Dynamic selection based on status of queue Selection based on individual customer attributes Number of customers waiting Round robin Priority Preemptive Processing time of customers (SPT rule) Queue Discipline

32. Queue Discipline • It is 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 customers.

33. continued • In medical setting, they use the procedure known as triage, 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 facilities • Priority – when the importance of customer decides the order of their service; example, an important customer may not stand in a line but be served personally by the manger.

34. continued • 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.

35. Service Process • The distribution of service times, arrangement of servers, management policies, and server behavior all contribute to service performance. • Service time can be a constant, such as the time to wash a car through an automated car wash. • Typically, the service time is not a constant, example, 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.

36. Service facility arrangement • Parallel servers – provides flexibility in meeting variation in 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 • Behavior of service providers is important for success. Under pressure, if provider speeds up, then some customers may interpret as bad quality.

37. 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

38. Arrival process Static Dynamic Random arrivals with constant rate Random arrival rate varying with time Facility- controlled Customer- exercised control Accept/Reject Price Appointments Reneging Balking Arrival Process (fig. 13.8)

39. Approaches to Controlling Customer Waiting • Animate: Disneyland distractions, elevator mirror, recorded music • Discriminate: Avis frequent renter treatment (out of sight) • Automate: Use computer scripts to address 75% of questions • Obfuscate: Disneyland staged waits (e.g. House of Horrors)

40. 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

41. Topics for Discussion • Suggest some strategies for controlling variability in service times. • 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?

42. 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.