Taylor Mgmt Science10

Introduction to Management Science, 10e (Taylor) Chapter 13 Queuing Analysis 1) Providing quick service is an important aspect of quality customer service. Answer: TRUE Diff: 1 Page Ref: 587 Main Heading: Elements of Waiting Line Analysis Key words: waiting lines 2) Operating characteristics describe the methods used by the service process. Answer: FALSE Diff: 2 Page Ref: 587 Main Heading: Elements of Waiting Line Analysis Key words: operating characteristics 3) Waiting lines form because people or things arrive at the servicing function, or server, faster than they can be served. Answer: TRUE Diff: 1 Page Ref: 587 Main Heading: Elements of Waiting Line Analysis Key words: waiting lines 4) Components of a waiting line system include arrivals, servers, and the calling population. Answer: FALSE Diff: 1 Page Ref: 588 Main Heading: The Single-Server Waiting Line System Key words: components of a waiting line 5) The most important factors to consider in analyzing a queuing system are queuing discipline, arrival and service rate, and the nature of the calling population. Answer: TRUE Diff: 3 Page Ref: 588 Main Heading: The Single-Server Waiting Line System Key words: queuing system 6) The queue discipline is the order in which waiting customers are served. Answer: TRUE Diff: 1 Page Ref: 589 Main Heading: The Single-Server Waiting Line System Key words: queuing discipline

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7) The calling population is the source of customers. Answer: TRUE Diff: 1 Page Ref: 589 Main Heading: The Single-Server Waiting Line System Key words: calling population 8) Calling populations are always finite. Answer: FALSE Diff: 1 Page Ref: 589 Main Heading: The Single-Server Waiting Line System Key words: calling population 9) The arrival rate is the frequency at which customers arrive at a waiting line according to a probability distribution. Answer: TRUE Diff: 1 Page Ref: 590 Main Heading: The Single-Server Waiting Line System Key words: arrival rate 10) The arrival rate is most frequently described by negative exponential distribution. Answer: FALSE Diff: 1 Page Ref: 590 Main Heading: The Single-Server Waiting Line System Key words: arrival rate, Poisson distribution 11) The service rate is the average time it takes to serve a customer. Answer: FALSE Diff: 1 Page Ref: 590 Main Heading: The Single-Server Waiting Line System Key words: service rate, exponential distribution 12) The service time can often be described by the Poisson distribution. Answer: FALSE Diff: 1 Page Ref: 590 Main Heading: The Single-Server Waiting Line System Key words: service rate, negative exponential distribution 13) Queuing system operating statistics are constant over time. Answer: TRUE Diff: 2 Page Ref: 592 Main Heading: The Single-Server Waiting Line System Key words: queuing system, steady state


14) As the level of service improves, the cost of service decreases. Answer: FALSE Diff: 1 Page Ref: 587 Main Heading: The Single-Server Waiting Line System Key words: service level 15) Queue discipline describes customers' behavior in the queue. Answer: FALSE Diff: 1 Page Ref: 589 Main Heading: Queuing Key words: queuing discipline 16) The basic single server queuing model assumes an infinite calling population. Answer: TRUE Diff: 1 Page Ref: 590 Main Heading: The Single-Server Waiting Line System Key words: queuing, calling population 17) Utilization of 100% is necessary for a queuing system to reach a steady state. Answer: FALSE Diff: 1 Page Ref: 590 Main Heading: The Single-Server Waiting Line System Key words: queuing systems, utilization 18) Queuing models provide optimal solutions to waiting line problems Answer: FALSE Diff: 1 Page Ref: 587 Main Heading: The Single-Server Waiting Line System Key words: queuing models, operating characteristics 19) All single-server queuing models require the utilization factor to be less than 1. Answer: TRUE Diff: 1 Page Ref: 590 Main Heading: The Single-Server Waiting Line System Key words: queuing system utilization 20) Queue discipline refers to the willingness of customers to wait in line for service. Answer: FALSE Diff: 1 Page Ref: 589 Main Heading: The Single-Server Waiting Line System Key words: queuing discipline


21) The basic single server model assumes that arrival rates are normally distributed. Answer: FALSE Diff: 1 Page Ref: 590 Main Heading: The Single-Server Waiting Line System Key words: single server waiting line syst, utilization rate, idle percent 22) A car wash with two attendants who work together as a team would be an example of a multiple-server system. Answer: FALSE Diff: 2 Page Ref: 601 Main Heading: Queuing Key words: single-server queuing model 23) In multiple server models, two or more servers work as a team to serve a single waiting line. Answer: FALSE Diff: 2 Page Ref: 607 Main Heading: Queuing Key words: multiple-server waiting line 24) In systems with finite queue length, the service rate does not have to exceed toe arrival rate. Answer: TRUE Diff: 2 Page Ref: 601 Main Heading: Queuing Key words: queuing system, finite queue length 25) The basic single server model assumes that customers who arrive first are served first. Answer: TRUE Diff: 2 Page Ref: 590 Main Heading: Queuing Key words: queuing discipline 26) If it takes 5 minutes to serve a customer at a fast food restaurant the service rate is _________. Answer: 12 customers per hour Diff: 2 Page Ref: 590 Main Heading: Queuing Key words: single server waiting line system, mean arrival rate 27) The __________ is the average number of customers who can be served during a given time period. Answer: service rate Diff: 2 Page Ref: 590 Main Heading: Queuing Key words: service rate


28) The service time can most often be described by the __________ distribution. Answer: negative exponential Diff: 2 Page Ref: 590 Main Heading: Queuing Key words: service time, negative exponential distribution 29) The __________ is the frequency at which the customers arrive at a waiting line according to a probability distribution. Answer: arrival rate Diff: 1 Page Ref: 590 Main Heading: Queuing Key words: arrival rate 30) The arrival rate can generally be described by a(n) __________ distribution. Answer: Poisson Diff: 2 Page Ref: 590 Main Heading: Queuing Key words: arrival rate, Poisson distribution 31) The __________ is the source of the customers or objects being simulated. Answer: calling population Diff: 2 Page Ref: 589 Main Heading: Queuing Key words: calling population 32) A system has one service facility that can service 10 customers per hour. The customers arrive at an average rate of 6 per hour. Utilization is __________. Answer: 60% Diff: 2 Page Ref: 591 Main Heading: Queuing Key words: utilization 33) A situation in which a mechanic is responsible for repairing a pool of fleet vehicles should be analyzed for a waiting line system with a __________ calling population Answer: Finite Diff: 1 Page Ref: 604 Main Heading: Queuing Key words: single server waiting line system, arrival rate 34) Customers arrive at a candy shop every 8 minutes on average. The arrival rate is __________. Answer: 7.5 customers per hour Diff: 1 Page Ref: 590 Main Heading: Queuing Key words: single server waiting line system, arrival rate


35) If λ = 24 and μ = 30, then utilization is equal to __________. Answer: 80% Diff: 1 Page Ref: 591 Main Heading: Queuing Key words: single server waiting model, utilization 36) If λ = 24 and μ = 30, then L is equal to __________. Answer: 4 customers Diff: 2 Page Ref: 591 Main Heading: Queuing Key words: single-server queuing model, avg wait time 37) If λ = 24 and μ = 30, then W is equal to __________ minutes. Answer: 10 Diff: 2 Page Ref: 591 Main Heading: Queuing Key words: single-server queuing model, avg wait time 38) If the __________ queuing system, which is a variation of the single phase single channel model, the service rate does not have to exceed the arrival rate. Answer: finite Diff: 2 Page Ref: 601 Main Heading: Queuing Key words: finite queue length 39) A single channel queuing system has an average service time of 10 minutes and an average time between arrivals of 15 minutes. What is the arrival rate? Answer: 4 per hour Diff: 1 Page Ref: 590 Main Heading: The Single Line Waiting Line System Key words: single server waiting line system, arrival rate 40) In a single server queuing system, if 10 customers arrive per hour, and 20 customers are served per hour, what is the probability that there are no customers in the system? Answer: 0.5 Diff: 1 Page Ref: 591 Main Heading: The Single Line Waiting Line System Key words: single server waiting line syst, utilization rate, idle percent


41) A single bay car wash with a Poisson arrival rate and an exponential service time has cars arriving an average of 15 minutes apart. It takes approximately 9 minutes to wash a car. What is the system utilization? Answer: 0.60 Diff: 1 Page Ref: 591 Main Heading: The Single Line Waiting Line System Key words: single server waiting line sys, utilization rate, sys utilization A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. 42) What is the utilization rate for the mechanic? Answer: 57% Diff: 1 Page Ref: 591 Main Heading: The Single Line Waiting Line System Key words: single server waiting model, utilization 43) What is the average time that a snowplow is out of service? Answer: .33 day or 2.64 hours Diff: 2 Page Ref: 591 Main Heading: The Single Line Waiting Line System Key words: single-server queuing model 44) On average, how long does a snow plow wait before the mechanic can begin his repair? Answer: 0.19 day or 1.25 hours Diff: 2 Page Ref: 591 Main Heading: The Single Line Waiting Line System Key words: single-server queuing model 45) Approximately how many vehicles are in the garage, waiting for or being repaired? Answer: 1.33 plows Diff: 2 Page Ref: 591 Main Heading: The Single Line Waiting Line System Key words: single-server queuing model


46) Poultry Processing processes chickens for fast food restaurants. The chickens arrive from the farms on trucks, in cages, at a rate of 8 trucks per hour according to the Poisson distribution. The quality standards of Poultry Processing require that the chickens be processes within 30 minutes, which includes the time from when the trucks arrive until the chickens are finished processing. Determine the maximum average processing rate (in truckloads per hour) that must be designed for the machine, in order to ensure that the cages will be processed, on the average, in 30 minutes or less. Assume processing time is exponentially distributed. Answer: μ = 10 trucks per hour Diff: 2 Page Ref: 591 Main Heading: The Single Line Waiting Line System Key words: single server waiting model, service rate Lenny, a graduate research assistant "moonlights" at the short order counter in the student union snack bar in the evenings. He is the only one on duty at the counter during the hours he works. Arrivals to the counter seem to follow the Poisson distribution with a mean of 8 per hour. Each customer is served one at a time and the service time follows an exponential distribution with a mean of 5 minutes. 47) How long will a student wait in line, on average? Answer: 0.167 hour or 10 minutes Diff: 1 Page Ref: 591 Main Heading: The Single Line Waiting Line System Key words: single server waiting model, utilization 48) The manager thinks that students will go elsewhere for lunch if they have to wait more than 5 minutes. Therefore he's thinking of hiring another server to help Lenny, reducing the customer service time to 4 minutes. How long will students wait in line if Lenny gets help? Answer: .076 hour or 4.56 minutes Diff: 2 Page Ref: 591 Main Heading: The Single Line Waiting Line System Key words: single server waiting model, queue length 49) Instead of having another student helps Lenny the manager is thinking of having two lines instead. Customers will equally divide themselves between the two lines. How long will students wait in line if there's a second server? (Assume that the service time is 5 minutes.) Answer: The arrival rate will be cut in half but the service rate remains the same. Waiting time in line is .04667 or 2.8 minutes. Diff: 3 Page Ref: 591 Main Heading: The Single Line Waiting Line System Key words: probability of full system, finite queue length


50) A hotel is considering changing its waiting line system. In the current system hotel guests divide themselves equally between the lines that form in front of 4 hotel clerks. The manager is considering having hotel guests wait in one line and then proceeding to the next available clerk. If average service time is 10 minutes and the average number of arrivals per hour is 12 guests, determine which system results in the lowest customer waiting time. Answer: Current system: λ = 12/4 = 3. W = .333 hour or 20 minutes. Proposed system: W = . 1812 or 10.8 minutes, so the proposed system results in less waiting time. Diff: 3 Page Ref: 591 Main Heading: The Multiple Channel Waiting Line System Key words: multiple channel waiting line system, average waiting time 51) The local grocery store consists of two cashiers. The customers arrive according to Poisson distribution and the service times are based on negative exponential distribution. The average customer service time is five minutes and the average time between the arrivals of successive customers is 3 minutes. What is the probability that there are no customers in the grocery store? Answer: P0 = .0909 Diff: 3 Page Ref: 591 Main Heading: The Multiple Channel Waiting Line System Key words: probability no customers in sys, multi channel waiting line sys The local grocery store consists of two cashiers. The customers arrive at the checkout according to the Poisson distribution and the service times are based on negative exponential distribution. The average customer service time is 4 minutes and the average time between the arrivals of successive customers is 3 minutes. Assume that customers equally divide themselves between the two cashiers. 52) What is the average number of customers waiting in each line and being checked out? Answer: L = 2 customers Diff: 3 Page Ref: 591 Main Heading: The Single Line Waiting Line System Key words: avg num of customers in the sys, multi channel waiting line sys 53) How much time is a customer expected to spend waiting in line and being checked out? Answer: W = 0.2 hour or 12 minutes Diff: 3 Page Ref: 591 Main Heading: The Single Line Waiting Line System Key words: avg time customer spends in sys, multi channel wait line sys 54) On average, how much time will the customer spend in line waiting to be served? Answer: Wq = .1333 hours or 8 minutes Diff: 3 Page Ref: 591 Main Heading: The Single Line Waiting Line System Key words: avg time customer spends in queue, multi channel wait line sys


55) On the average, how many customers are waiting in line to be served? Answer: Lq = 1.33 customers Diff: 3 Page Ref: 591 Main Heading: The Single Line Waiting Line System Key words: avg num of customers in queue, multi channel waiting line sys 56) A queuing system has 3 crews with 2 members each. What is the number of servers? Answer: 3 Diff: 1 Page Ref: 591 Main Heading: The Single Line Waiting Line System Key words: multiple channel waiting line system, number of servers 57) A multiple channel queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 6 customers per hour and an average service time of 20 minutes per customer. What is the minimum number of servers required to avoid an overloaded system? Answer: 3 Diff: 2 Page Ref: 608 Main Heading: The Multiple Channel Waiting Line System Key words: multiple channel waiting line system, number of servers In a factory machines breakdown at an average of 6 machines per hour according to a Poisson distribution. The time a repair person takes to repair the machine is not defined by any probability distribution but has a mean of 8 minutes and a standard deviation of 3 minutes. 58) What is the probability that no machine is being fixed? Answer: P0 = 1 - .8 = .2 Diff: 2 Page Ref: 599 Main Heading: Undefined and Constant Service Times Key words: probability of no customers in sys, undef/constant service times 59) On the average how many machines are waiting in line to be fixed? Answer: Lq = .144 machines Diff: 3 Page Ref: 599 Main Heading: Undefined and Constant Service Times Key words: avg num of custs waiting in line, undefined/constant service times 60) On the average, how many machines are in the system either being repaired or waiting in line to be repaired? Answer: L = .944 machines Diff: 3 Page Ref: 599 Main Heading: Undefined and Constant Service Times Key words: avg num of customers in the system, undefined and constant service times


61) On the average, how long will a machine have to wait before it is fixed? Answer: Wq = 1.44 minutes Diff: 3 Page Ref: 599 Main Heading: Undefined and Constant Service Times Key words: average time spent in queue, undefined/constant service times 62) On the average, how long will a machine be down and out of service? Answer: W = 9.44 minutes Diff: 3 Page Ref: 599 Main Heading: Undefined and Constant Service Times Key words: average time spent in system, undefined/constant service times In a bank drive-through, there is a single service window and room only for 2 cars to line-up to wait for service. The mean time between arrivals for drive through customers is five minutes. The mean time to complete a customer transaction is 3 minutes. The number of arrivals is distributed according to Poisson distribution and the service times are exponentially distributed. 63) What is the probability that there are no vehicles in the system? Answer: P0 = .4105 Diff: 3 Page Ref: 601 Main Heading: Finite Queue Length Key words: probability no customers in the system, finite queue length 64) On the average how many cars are in the system? Answer: L = 1.3949 cars Diff: 3 Page Ref: 601 Main Heading: Finite Queue Length Key words: number of customers in the system, finite queue length 65) What is the probability that the system is full and the customer must drive on? Answer: PM = .0887 Diff: 3 Page Ref: 601 Main Heading: Finite Queue Length Key words: the probability that the system is full, finite queue length 66) On the average, how many customers are waiting to be served? Answer: Lq = .84812 cars Diff: 3 Page Ref: 601 Main Heading: Finite Queue Length Key words: number of customers in the waiting line, finite queue length


67) What is the average time a customer spends in the system? Answer: W = 7.653 minutes Diff: 3 Page Ref: 601 Main Heading: Finite Queue Length Key words: the avg time customer spends in system, finite queue length 68) What is the average time a customer spends in the line waiting to be served? Answer: Wq = 4.653 minutes Diff: 3 Page Ref: 601 Main Heading: Finite Queue Length Key words: avg time customer spends in waiting line, finite queue length 69) Operating characteristics for a waiting line system include A) queue discipline B) the Poisson distribution C) a waiting line structure D) utilization Answer: D Diff: 1 Page Ref: 587 Main Heading: The Single-Server Waiting Line System Key words: single server waiting line system, components of a waiting line 70) The most important factors to consider in analyzing a queuing system are A) the queue discipline B) the queue structure C) the queue order D) all of the above Answer: A Diff: 3 Page Ref: 589 Main Heading: The Single-Server Waiting Line System Key words: queuing system, queuing discipline 71) Customers may be served A) according to a number assigned to each item B) on a first-come-first serve basis C) on a last-come-first-serve basis D) all of the above Answer: D Diff: 2 Page Ref: 589 Main Heading: The Single-Server Waiting Line System Key words: queuing system, queuing discipline


72) In a single-server queuing model, L represents A) the length of time a customer waits B) the size of the queue C) the average number of customers in the queuing system D) the length of the line Answer: C Diff: 1 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: single-server queuing model 73) Operating characteristics A) are averages B) are constant over time C) represent the steady state D) all of the above Answer: D Diff: 2 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: single-server queuing model 74) Queuing discipline refers to the A) reason waiting occurs in underloaded systems B) willingness of customers to wait in line C) order in which customers are processed D) all of the above Answer: C Diff: 2 Page Ref: 589 Main Heading: The Single-Server Waiting Line System Key words: queuing discipline 75) The arrival rate is the A) time between arrivals to the service facility B) rate items arrive at the server after being in queue C) rate of arrivals to the service facility D) all of the above Answer: C Diff: 2 Page Ref: 590 Main Heading: The Single-Server Waiting Line System Key words: arrival rate


76) A single server queuing system has average time between arrivals of 20 minutes and a service time of 10 minutes each. Assuming Poisson arrivals and exponential service times, the utilization factor is approximately A) 0.25 B) 0.33 C) 0.50 D) 0.67 E) 2.0 Answer: C Diff: 2 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: single server waiting model, utilization 77) What happens to the customer waiting time if system utilization increases? A) decreases exponentially B) decreases proportionally C) increases proportionally D) increases exponentially Answer: D Diff: 2 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: system utilization, customer waiting time 78) What is not considered a measure of system performance in a queuing analysis? A) average number in the system B) system utilization C) average number waiting in line D) service time Answer: D Diff: 2 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: queuing analysis, system performance 79) Which of the following will not decrease system utilization? A) increase in arrival rate B) increase in service rate C) increase in the number of servers D) decrease in service time Answer: A Diff: 2 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: system utilization


A single server waiting line system has an arrival pattern characterized by a Poisson distribution with 3 customers per hour. The average service time is 12 minutes. The service times are distributed according to the negative exponential distribution. 80) The average time a customer can expect to wait in line is: A) 18 minutes B) 36 minutes C) 30 minutes D) 60 minutes E) 72 minutes Answer: A Diff: 2 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: average waiting time, single server waiting line 81) The probability that the system is idle is: A) 0 B) .20 C) .40 D) .60 E) .80 Answer: C Diff: 2 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: probability that system is idle, single server waiting line 82) The expected number of customers in the system is: A) 3.0 B) 1.5 C) 1.0 D) .90 E) .60 Answer: B Diff: 2 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: number of customers in the system, single server waiting line


83) The expected number of customers in the waiting line is: A) .6 B) .7 C) .8 D) .9 E) 1.0 Answer: D Diff: 2 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: number of customers in wait line, single server waiting line 84) A system has 5 servers. Customers arrive at a rate of 6 per hour and service time is 20 minutes. What is the system utilization? A) .83 B) .40 C) .50 D) 20 Answer: B Diff: 2 Page Ref: 607 Main Heading: Queuing Key words: multiple-server waiting line A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. 85) The utilization is A) .30 B) .45 C) .57 D) .85 E) 1.00 Answer: C Diff: 2 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: single server waiting model, utilization


86) Determine the average time that a snowplow is out of service. A) .33 hours B) 20 minutes C) 2.64 hours D) .33 days E) 1.15 hours Answer: C Diff: 2 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: expected waiting time in the queue, single server waiting line sys 87) On average, how long does a plow wait before the mechanic begins the repair? A) 1 hour B) 1.25 hours C) 1.52 hours D) 2 hours E) 2.64 hours Answer: C Diff: 2 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: expected num of customers in sys, single server waiting line sys 88) What is the expected average number of snowplow in the garage (waiting for repair and being repaired)? A) 1 B) 1.33 C) 2 D) 2.52 Answer: B Diff: 3 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: multi server waiting line, expected avg num of customers in sys 89) In a single server queuing system, if 12 customers arrive per hour, and 30 customers are served per hour, what is the probability that there are no customers in the system? A) 0.75 B) 0.60 C) 0.40 D) 0.2 5 Answer: B Diff: 1 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: single server queuing sys, probability no customers in the sys


90) A manager is trying to improve a single-server queueing system through automation. The average service time is 20 minutes per customer, exponentially distributed, and the arrival rate is 16 customers per 8-hour day (Poisson arrivals). The automated system will have a constant service time of 16 minutes. The effect of this change will: A) decrease utilization B) increase waiting time C) decrease waiting time D) have no effect since the service time is unchanged Answer: C Diff: 2 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: constant service times 91) A multiple channel system has customers arriving at an average rate of 5 per hour and an average service time of 40 minutes. What minimum number of servers is required to ensure that the system is not overloaded? A) 4 B) 5 C) 6 D) 3 Answer: A Diff: 1 Page Ref: 607 Main Heading: The Single-Server Waiting Line System Key words: The multiple server waiting line 92) A single channel queuing system has an average service time of 8 minutes and an average time between arrivals of 10 minutes. What is the hourly arrival rate? A) 8 B) 6 C) 4 D) 2 Answer: B Diff: 1 Page Ref: 590 Main Heading: The Single-Server Waiting Line System Key words: the single server waiting line, arrival rate 93) A queuing system has 5 crews with 2 members each. What is the number of servers? A) 2 B) 5 C) 10 D) none of the above Answer: B Diff: 1 Page Ref: 592 Main Heading: The Single-Server Waiting Line System Key words: the number of servers


94) A multiple channel queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 4 customers per hour and an average service time of 18 minutes per customer. What is the minimum number of servers required to avoid an overloaded system? A) 1 B) 2 C) 3 D) 4 Answer: B Diff: 1 Page Ref: 607 Main Heading: Queuing Key words: number of servers 95) Poultry Processing processes chickens for fast food restaurants. The chickens arrive from the farms on trucks, in cages, at a rate of 8 trucks per hour according to the Poisson distribution. The quality standards of Poultry Processing require that the chickens be processes within 30 minutes, which includes the time from when the trucks arrive until the chickens are finished processing. What is the maximum average processing rate (in truckloads per hour) that must be designed for the machine, in order to ensure that the cages will be processed, on the average, in 30 minutes or less. Assume processing time is exponentially distributed. A) 4.5 trucks per hour B) 9 trucks per hour C) 10 trucks per hour D) 18 trucks per hour Answer: C Diff: 2 Page Ref: 591 Main Heading: The Single-Server Waiting Line System Key words: single server waiting model, service rate 96) Constant service times occur with A) machinery B) well-trained employees C) service processes D) assembly processes Answer: A Diff: 2 Page Ref: 600 Main Heading: Undefined and Constant Service Times Key words: constant service times


97) Customers arrive at a music store at an average of 1 per minute (Poisson arrivals). The service rate is 15 customers per hour (exponential service times). What is the minimum number of servers needed to keep the waiting time in the system under 5 minutes? A) 4 B) 5 C) 6 D) 7 Answer: C Diff: 3 Page Ref: 607 Main Heading: Queuing Key words: multiple channel waiting line system, average waiting time 98) A single bay car wash with a Poisson arrival rate and an exponential service time has cars arriving on average of 10 minutes apart and an average service time of 4 minutes. What is the system utilization? A) 0.2 B) 0.3 C) 0.4 D) 0.5 E) 0.6 Answer: C Diff: 1 Page Ref: 599 Main Heading: Undefined and Constant Service Times Key words: system utilization 99) Cars arrive at a single bay car wash on the average of 6 per hour according to the Poisson distribution. The wash time is a constant 4 minutes. What is the average number of cars in line? A) .022 B) .133 C) .267 D) .667 Answer: B Diff: 2 Page Ref: 600 Main Heading: Undefined and Constant Service Times Key words: constant service time, queue length


100) Cars arrive at a single bay car wash on the average of 6 per hour according to the Poisson distribution. The wash time averages 4 minutes with a standard deviation of 1 minute, but the wash time is not defined by any distribution. What is the average number of cars in line? A) .142 B) .267 C) .283 D) 2.83 E) 3.33 Answer: A Diff: 2 Page Ref: 599 Main Heading: Undefined and Constant Service Times Key words: undefined service time 101) In a finite queue, the length of the queue is A) limited B) unlimited C) limited or unlimited D) limited and unlimited Answer: A Diff: 2 Page Ref: 601 Main Heading: Finite Queue Length Key words: finite queue 102) Pickmeup is a drive through coffee house that has room for 3 cars in the driveway. The line cannot exceed 3 cars, and because they are exclusively drive through, customers may be turned away. In the morning, the arrival rate is 40 cars per hour (Poisson distributed) and with the servers working in teams, they can process 50 cars per hour (The service rate is exponential). What is the probability of turning customers away? A) .173 B) .210 C) .339 D) .410 Answer: A Diff: 3 Page Ref: 591 Main Heading: Finite Queue Length Key words: probability of full system, finite queue length


103) In multiple-server models, __________ independent servers in parallel serve a single waiting line. A) 2 or more B) 3 or more C) 4 or more D) 5 or more Answer: A Diff: 2 Page Ref: 607 Main Heading: The Multiple-Server Waiting Line Key words: multiple-server waiting line The local grocery store consists of two cashiers. The customers arrive at the checkout according to the Poisson distribution and the service times are based on negative exponential distribution. The average customer service time is 4 minutes and the average time between the arrivals of successive customers is 3 minutes. Assume that customers equally divide themselves between the two cashiers. 104) How much time is a customer expected to spend in line at the checkout? A) 11.2 minutes B) 13.6 minutes C) 14.4 minutes D) 16.2 minutes E) 18.2 minutes Answer: D Diff: 3 Page Ref: 591 Main Heading: The Multiple-Server Waiting Line Key words: avg time customer spends in sys, multi channel wait line sys 105) On the average, how much time will the customer spend in line waiting to be served? A) 11.2 minutes B) 13.6 minutes C) 14.4 minutes D) 16.2 minutes E) 18.2 minutes Answer: A Diff: 3 Page Ref: 591 Main Heading: The Multiple-Server Waiting Line Key words: avg time customer spends in queue, multi channel wait line sys


106) What is the probability that there are no customers in the grocery store? A) .0809 B) .0909 C) .10909 D) .1209 E) .1409 Answer: B Diff: 3 Page Ref: 591 Main Heading: The Multiple-Server Waiting Line Key words: probability no customers in sys, multi channel waiting line sys


Taylor Mgmt Science10

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