Waiting Lines and Queuing Theory Models lCHAPTER 14
TRUE/FALSE
14.1 The three parts of a queuing system are the arrivals, the queue, and the service facility.
14.2 Two characteristics of arrivals are the line length and queue discipline.
14.3 Queuing theory models can also apply to customers placing telephone calls and being placed on hold.
14.4 The only objective of queuing theory is to minimize customer dissatisfaction.
14.5 Should a customer leave a queue before being served, it is said that the customer has reneged.
14.6 Balking refers to customers who enter the queue but may become impatient and leave without completing their transactions.
14.7 Most systems use the queue discipline known as the first-in, first-out rule.
14.8 In a very complex queuing model, if all of the assumptions of the traditional models are not met, then the problem cannot be handled.
14.9 Before using exponential distributions to build queuing models, the quantitative analyst should determine if the service time data fit the distribution.
14.10 For practical purposes, queue length is almost always modeled with a finite queue length.
14.11 The Greek letter l is used to represent the average service rate at each channel.
14.12 For a single channel model that has Poisson arrivals and exponential service rates, the Greek letter r is the utilization factor.
14.13 In a multi-channel, single-phase queuing system, the arrival will pass through at least two different service facilities.
14.14 In a multi-channel model r = l /( M m).
14.15 A goal of many waiting line problems is to help a firm find the ideal level of services to be offered.
14.16 Any waiting line problem can be investigated using an analytical queuing model.
14.17 One of the difficulties in waiting line analyses is that it is sometimes difficult to place a value on customer waiting time.
14.18 The goal of most waiting line problems is to identify the service level that minimizes service cost.
14.19 One of the limitations of analytical waiting line models is that they do not give information on extreme cases (e.g., maximum waiting time or maximum number in the queue).
14.20 An "infinite calling population" occurs when the likelihood of a new arrival does not depend upon the number of past arrivals.
14.21 All practical problems can be described by an "infinite" population waiting model.
14.22 On a practical note – if we are using waiting line analysis for a problem studying customers calling a telephone number for service, balking is probably not an issue.
14.23 On a practical note– if we are using waiting line analysis to study cars passing through a single tollbooth, reneging is probably not an issue.
14.24 On a practical note – if we are studying patrons moving through checkout lines at a grocery store, and we note that these patrons sometimes move from one line to another, we should consider balking as an issue.
14.25 On a practical note – if we were to study the waiting lines in a hair salon which had only five chairs for patrons waiting, we would have to use a finite queue waiting line model.
14.26 All practical waiting line problems can be viewed as having a FIFO queue discipline.
14.27 A hospital emergency room will usually employ a FIFO queue discipline.
14.28 If we wish to study a bank, in which patrons entered the building and then, depending upon the service desired, chose one of several tellers in front of which to form a line, we would employ a set of single-channel queuing models.
14.29 On a practical note – we should probably view the checkout counters in a grocery store as a set of single channel systems.
14.30 A cafeteria, in which cold dishes are separated from hot dishes, is probably best viewed as a single-channel, single-phase system.
14.31 An emergency room might be viewed as a multi-channel, multi-phase system.
14.32 A single highway with multiple tollbooths should be viewed as a single-channel system.
14.33 In a doctor's office, we would expect the arrival rate distribution to be Poisson distributed, and the service time distribution to be negative exponential.
14.34 The M/M/1 queuing model assumes that the arrival rate does not change over time.
14.35 The analytical queuing models typically provide operating characteristics that are averages (e.g., average waiting time, average number of customers in the queue).
14.36 The analytical queuing models can be used to tell us how many people are presently waiting in line.
14.37 The quantity r is the probability that one or more customers are in a single channel system.
14.38 In the multi-channel model (M/M/m), we must assume that the average service time for all channels is the same.
14.39 If we compare a single-channel system with l = 15, to a multi-channel system (with 3 channels) with the service rate for the individual channel of l = 5, we will find that the average wait time is less in the singlechannel system.
14.40 If we compare a single-channel system with exponential service rate (l=5) to a constant service time model (l=5), we will find that the average wait time in the constant service time model is less than that in the probabilistic model.
14.41 As a general rule, any time that the number of people in line can be a significant portion of the total population, we should use a finite population model.
14.42 Whether or not we use the finite population queuing model depends upon the relative arrival and service rates, not just the size of the population from which the arrivals come.
14.43 Whether or not we use the finite population queuing model depends upon the amount of space we have in which to form the queue.
14.44 If a waiting line problem is particularly complex, we may have to turn to a simulation model.
14.45 If we are using a simulation queuing model, we still have to abide by the assumption of a Poisson arrival rate, and negative exponential service rate.
14.46 Using a simulation model allows one to ignore the common assumptions required to use analytical models.
*14.47 If we are studying the arrival of automobiles at a highway toll station, we can assume an infinite calling population.
*14.48 If we are studying the need for repair of electric motors on a small assembly line, we can assume an infinite calling population.
*14.49 The difference between balking and reneging is that balking implies that the arrival never joined the queue, while reneging implies that the arrival joined the queue, but became impatient and left.
*14.50 When looking at the arrivals at the ticket counter of a movie theater, we can assume an unlimited queue.
*14.51 When looking at the arrivals at a barbershop, we must assume a finite queue.
*14.52 A bank, in which a single queue is used to move customers to several tellers, is an example of a single-channel system.
*14.53 A fast food drive-through system is an example of a multi-channel queuing system.
*14.54 A fast food drive-through system is an example of a multi-phase queuing system.
*14.56 In a single-channel, single-phase system, reducing the service time only reduces the total amount of time spent in the system, not the time spent in the queue.
*14.57 The wait time for a single-channel system is more than twice that for a two channel system using two servers working at the same rate as the single server.
MULTIPLE CHOICE
14.58 The expected cost to the firm of having customers or objects waiting in line to be serviced is termed the
(a) expected service cost.
(b) expected waiting cost.
(c) total expected cost.
(d) expected balking cost.
(e) expected reneging cost.
14.59 Which of the following is not an assumption in common queuing mathematical models?
(a) Arrivals come from an infinite, or very large, population.
(b) Arrivals are Poisson distributed.
(c) Arrivals are treated on a first-in, first-out basis and do not balk or renege.
(d) Service times follow the negative exponential distribution.
(e) The average arrival rate is faster than the average service rate.
14.60 Which of the following is not a key operating characteristic for a queuing system?
(a) utilization rate
(b) percent idle time
(c) average time spent waiting in the system and in the queue
(d) average number of customers in the system and in the queue
(e) none of the above
14.61 Three parts of a queuing system are
(a) the inputs, the queue, and the service facility.
(b) the calling population, the queue, and the service facility.
(c) the calling population, the waiting line, and the service facility.
(d) All of the above are appropriate labels for the three parts of a queuing system.
14.62 Upon arriving at a convention, if a person must line up to first register at a table, then proceed to a table to gather some additional information, and then pay at another single table, this is an example of a
(a) single-channel, multi-phase system.
(b) single-channel, single-phase system.
(c) multi-channel, multi-phase system.
(d) multi-channel, single-phase system.
(e) none of the above
14.63 The utilization factor r for a system is defined as
(a) the mean number of people served divided by the mean number of arrivals per time period.
(b) the average time a customer spends waiting in a queue.
(c) the proportion of the time the service facilities are in use.
(d) the percent idle time.
(e) none of the above
14.64 Which of the following is not a characteristic of the calling population and its behavior?
(a) Size is considered to be limited or unlimited.
(b) Queue discipline.
(c) A customer is usually patient.
(d) Customers can arrive randomly.
(e) none of the above
14.65 In queuing theory, the objective is to
(a) maximize productivity.
(b) minimize customer dissatisfaction as measured in balking and reneging.
(c) minimize the sum of the costs of waiting time and providing service.
(d) minimize the percent of idle time.
(e) minimize queue length.
14.66 In queuing problems, the size of the calling population is important because
(a) it is usually easier to deal with the mathematics if the calling population is considered infinite.
(b) it is usually easier to deal with the mathematics if the calling population is considered finite.
(c) it is impossible to deal with the mathematics (except through monte carlo simulation) if the calling population is infinite.
(d) it is impossible to deal with the mathematics (except through monte carlo simulation) if the calling population is finite.
(e) none of the above
14.67 An arrival in a queue that reneges is one who
(a) after joining the queue, becomes impatient and leaves.
(b) refuses to join the queue because it is too long.
(c) goes through the queue, but never returns.
(d) jumps from one queue to another, trying to get through as quickly as possible.
(e) none of the above
14.68 A balk is an arrival in a queue who
(a) refuses to join the queue because it is too long.
(b) after joining the queue, becomes impatient and leaves.
(c) goes through the queue, but never returns.
(d) jumps from one queue to another, trying to get through as quickly as possible.
14.69 Queue discipline may be
(a) FIFO (first-in, first-out).
(b) FIFS (first-in, first-served).
(c) LIFS (last-in, first-served).
(d) by assigned priority.
(e) all of the above
14.70 If the arrival rate and service times are kept constant and the system is changed from a singlechannel to a two-channel system, then the average time an arrival will spend in the waiting line or being serviced (W) is
(a) increased by 50 percent.
(b) reduced by 50 percent.
(c) exactly doubled.
(d) the same.
(e) none of the above
14.71 If everything else remains constant, including the mean arrival rate and service rate, except that the service time becomes constant instead of exponential,
(a) the average queue length will be halved.
(b) the average waiting time will be doubled.
(c) the average queue length will increase.
(d) the average queue length will double and the average waiting time will double.
(d) none of the above
14.72 If a queuing situation becomes extremely complex,
(a) there is always a mathematical model to solve it.
(b) the only alternative is to study the real situation.
(c) there are tables available for any combination of complexities.
(d) computer simulation is an alternative.
(e) you should make simplifying assumptions and use the mathematical procedure which most closely approximates the system to be studied.
14.73 Customers enter the waiting line at a cafeteria on a first come, first served basis. The arrival rate follows a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is six per minute and the average service rate of a single server is eight per minute, what is the average number of customers in the system?
(a) 0.50
(b) 0.75
(c) 2.25
(d) 3.00
(e) none of the above
14.74 Customers enter the waiting line at a cafeteria on a first come, first served basis. The arrival rate follows a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is six per minute and the average service rate of a single server is eight per minute, what is the average number of customers waiting in line behind the person being served?