MGT 2251 Final Test Bank
95) At an automatic car wash, cars arrive randomly at a rate of 7 cars every 30 minutes. The car wash takes exactly 4 minutes (this is constant). On average, what would be the length of the line?
A) 8.171B) 7.467C) 6.53D) 0.467E) None of the above Answer: C
69) Most systems use a queue discipline known asA) shortest processing time.B) longest processing time.C) FIFO.D) earliest due date.E) critical ratio.
Answer: C
133) At the start of football season, the ticket office gets busy the day before the first game. Customers arrive at the rate of four every ten minutes. A ticket seller can service a customer in four minutes. Traditionally, there are two ticket sellers working. The university is considering an automated ticket machine similar to the airlines' e-ticket system. The automated ticket machine can service a customer in 2 minutes.a) What is the average length of the queue for the in-person model?(b) What is the average length of the queue for the automated system model?(c) What is the average time in the system for the in-person model?(d) What is the average time in the system for the automated system model?(e) Assume the ticket sellers earn $8 per hour and the machine costs $20 per hour (amortized over 5 years). The wait time is only $4 per hour because students are patient. What is the total cost of each model?
Answer: (a) Lq = 2.844(b) Lq = 1.6(c) W = 0.1852 hour or 11.11 minutes(d) W = 0.1 hour or 6 minutes(e) Total cost (in-person) = (2 ∗ $8/hour) + (24/hour ∗ .1852 hours) ($4/hour) = $33.78 Total cost (automated) = (1 ∗ $20/hour) + (24/hour ∗ .1 hour) ($4/hour) = $29.60
64) Customers enter the waiting line to pay for food as they leave 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 four per minute and the average service rate of a single server is seven per minute, what proportion of the time is the server busy?A) 0.43B) 0.57C) 0.75D) 0.25E) 0.33
Answer: B
73) A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. What type of queuing model applies here?A) M/M/1B) M/M/2C) M/D/2D) M/D/1E) M/G/1
Answer: B
75) A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. What is the average length of the line?A) 3.429B) 1.929C) 1.143D) 0.643E) None of the above
Answer: B
43) Which of the following is not a valid queuing model based on the Kendall notation?A) M/M/3B) D/D/2C) D/M/1D) M/M/0E) G/D/1
Answer: D
56) The "utilization factor" is defined as theA) percent of time the system is idle.B) average percent of time the customers wait in line.C) average time the service system is open.D) percent of time that a single customer is in the system.E) None of the above
Answer: E
74) A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an normal distribution. What type of queuing model applies here?A) M/M/1B) M/M/2C) M/D/2D) M/D/1E) M/G/2
Answer: E
78) According to the information provided in Table 12-1, on average, how many units are in the line?A) 1.646B) 0.563C) 0.280D) 1.125E) 0.521
Answer: E
86) Cars arrive at a local JLUBE franchise at the rate of 1 every 12 minutes. Service times are exponentially distributed with an average of 15 minutes. Jack Burns, the JLUBE owner, has decided to open a second work bay, i.e., make the shop into a two-channel system. Under this new scheme, the total time an average customer spends in the system will beA) 37 minutes.B) 2.1 minutes.C) 9.6 minutes.D) 33.3 minutes.E) 24.6 minutes.
Answer: E
129) Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school. Sam can vaccinate a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of 1 dog every 6 minutes, according to a Poisson distribution. Also assume that Sam's vaccinating times are exponentially distributed. Sam would like to have each waiting dog placed in a holding pen. If Sam wants to be certain he has enough cages to accommodate all dogs at least 90 percent of the time, how many cages should he prepare?
Answer: He needs to prepare 2 cages. The probability of having more than 3 dogs in the system is 0.0625 while the probability of having more than 2 dogs in the system is 0.125.
144) What is meant by a multiphase system?
Answer: Service is provided at more than one station, one after the other.
128) A dry cleaner has a single drive-thru window for customers. The arrival rate of cars follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is 16 per hour and the average service time is three minutes. If the dry cleaner wants to accommodate (have enough room for) all of the waiting cars at least 96 percent of the time, how many car-lengths should they make the driveway leading to the window?
Answer: The probability of having more than 14 cars in the system is (16/20)14+1 = 0.035, so they should make the driveway approximately 13 car-lengths long (because one car will be at the service window). (The probability of having more than 13 cars in the system is 0.044 (which is too high), and the percentage only gets worse as the queue length is shortened.)
145) What is the steady state of a queuing system?
Answer: The steady state is the normal operating condition of a queuing system.
139) With regard to queuing theory, define what is meant by balking.
Answer: This refers to the situation when arriving customers choose to not enter the queue because it is too long to suit their needs or interests.
142) What is meant by a multichannel queuing system?
Answer: more than one service facility all fed by the same queue
141) What is meant by a single-channel queuing system?
Answer: one service facility system fed by one queue
140) With regard to queuing theory, define what is meant by reneging.
Answer: the situation when customers in a queue choose to leave the queue before getting service
127) A dry cleaner has a single drive-thru window for customers. The arrival rate of cars follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is 16 per hour and the average service time is three minutes.(a) What is the average number of cars in the line?(b) What is the average time spent waiting to get to the service window?(c) What percentage of time is the dry cleaner's drive-thru window idle?d) What is the probability there are more than 2 cars at the drive-thru window?
Answer: (a) Lq = 3.2(b) Wq = 0.2 hour (12 minutes)(c) Po = 0.20(d) Pn > k = 0.512
126) Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school. Sam can vaccinate a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of 1 dog every 4 minutes, according to a Poisson distribution. Also assume that Sam's vaccinating times are exponentially distributed. (a) Find the probability that Sam is idle.b) Find the proportion of time that Sam is busy.(c) Find the average number of dogs receiving or waiting to be vaccinated.(d) Find the average number of dogs waiting to be vaccinated.(e) Find the average time a dog waits before getting vaccinated.(f) Find the average amount (mean) of time a dog spends between waiting in line and getting vaccinated.
Answer: (a) Po = 0.25(b) ρ = 0.75(c) L = 3(d) Lq = 2.25(e) Wq = 0.15 hour(f) W = 0.2 hour
125) Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school. Sam can vaccinate a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of 1 dog every 6 minutes, according to a Poisson distribution. Also assume that Sam's vaccinating times are exponentially distributed. (a) Find the probability that Sam is idle.(b) Find the proportion of time that Sam is busy.(c) Find the average number of dogs receiving or waiting to be vaccinated.(d) Find the average number of dogs waiting to be vaccinated.(e) Find the average time a dog waits before getting vaccinated.(f) Find the average amount (mean) of time a dog spends between waiting in line and getting vaccinated.
Answer: (a) Po = 0.5(b) ρ = 0.5(c) L = 1(d) Lq = 0.5(e) Wq = 0.05 hour(f) W = 0.1 hour
131) Cars arrive at a parking lot entrance at the rate of 20 per hour. The average time to get a ticket and proceed to a parking space is two minutes. There are two lot attendants at the current time. The Poisson and exponential distribution appear to be relevant in this situation.(a) What is the probability that an approaching auto must wait?(b) What is the average waiting time?(c) What is the average number of autos waiting to enter the garage?
Answer: (a) Po = 0.50(b) Wq = 0.25 minute(c) Lq = 0.0833 auto
124) A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 15 per hour. It takes exactly two minutes to answer each question. It is assumed that arrivals are Poisson.(a) Find the probability that the employee is idle.(b) Find the proportion of time that the employee is busy.(c) Find the average number of people receiving and waiting to receive information.(d) Find the average number of people waiting in line to get information.(e) Find the average time a person seeking information spends at the desk. f) Find the expected time a person spends waiting in line to have his question answered.
Answer: (a) Po = 0.50(b) ρ = 0.50(c) L = 0.75(d) Lq = 0.25(e) W = 0.05 hour(f) Wq = 0.03 hour
123) A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 15 per hour. It takes an average of two minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed.(a) Find the probability that the employee is idle.(b) Find the proportion of time that the employee is busy.(c) Find the average number of people receiving and waiting to receive information.(d) Find the average number of people waiting in line to get information.(e) Find the average time a person seeking information spends at the desk.(f) Find the expected time a person spends waiting in line to have his question answered.
Answer: (a) Po = 0.50(b) ρ = 0.50(c) L = 1(d) Lq = 0.50(e) W = 0.0667 hour(f) Wq = 0.0333 hour
132) Bank Boston has a branch at Bryant College. The branch is busiest at the beginning of the college year when freshmen and transfer students open accounts. This year, freshmen arrived at the office at a rate of 40 per day (8-hour day). On average, it takes the Bank Boston staff person about ten minutes to process each account application. The bank is considering having one or two tellers. Each teller is paid $12 per hour and the cost of waiting in line is assumed to be $8 per hour.(a) What is the total daily waiting cost for the single teller model?(b) What is the total daily waiting cost for the two-teller model?(c) What is the total daily service cost for the single teller model?(d) What is the total daily service cost for the two-teller model?(e) Which model is preferred?
Answer: (a) Total wait cost = [(5 * .833 hours) (8)] * 8 hours/day = $266.56(b) Total wait cost = [(5 * .035 hours) (8)] * 8 hours/day = $11.20(c) Total service cost = (1 * $12) * 8 hours/day = $96(d) Total service cost = (2 * $12) * 8 hours/day = $192(e) Two channel model
138) Customers at a DMV arrive at a rate of 45 per hour. There are three servers that can process customers at an average of 3 minutes. (a) What is the average wait time?(b) What is the average number of customers waiting?(c) What is the average number of customers in the DMV?
Answer: (a) Wq = 0.04 hour(b) Lq = 1.70(c) L= 3.95
137) Customers arrive at a bank at a rate of 50 per hour. The bank has 3 tellers and on average, it takes 2 minutes to service a customer. (a) What proportion of time are the tellers busy?(b) What is the average number of customers in the bank?(c) What is the average weight time?
Answer: (a) ρ = 0.55(b) L = 2.04(c) Wq = 0.0075 hour
130) A new shopping mall is considering setting up an information desk operated by two employees. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 20 per hour. It takes an average of 4 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed.(a) Find the proportion of the time that the employees are busy.(b) Find the average number of people waiting in line to get some information.(c) Find the expected time a person spends just waiting in line to have his question answered.
Answer: (a) ρ = 0.667(b) Lq = 1.0667(c) Wq = 0.0533 hour
136) A professor decides to hold a three hour window open for student advising. The professor has 15 advisees. He's unsure if each advisee will show up, and its possible that a single advisee could show up multiple times during the 3 hour window. On average, the professor will spend 12 minutes with each student. He usually expects each student to arrive once during the 3 hour window.(a) What proportion of the time can the professor expect to be busy during the window?(b) What is the expected number of students in queue during the window?(c) What is the expected wait time in queue during the window?
Answer: (a) ρ = 0.82(b) Lq = 1.88(c) Wq = 0.46 hour
135) There is a tutoring lab at a university that holds 20 students. Due to the popularity of the 3 tutors, the lab is always at capacity. Each student approaches a tutor an average of 2 times per hour, and a tutor spends on average 5 minutes per question from a student. The service time follows an exponential distribution.(a) What proportion of the time are the tutors busy?(b) What is the average waiting time for students in queue?
Answer: (a) ρ = 0.86(b) Wq = 0.06 hour
134) Consider a single-server queuing system with Poisson arrivals of 10 units per hour and a constant service time of 2 minutes per unit. How long will the customer waiting time be in seconds, on average?
Answer: 10 / [(2)(30)(30 − 10)] = .00833333 hours = 0.5 minute = 30 seconds
102) According to the information provided in Table 12-4, which presents a queuing problem solution for a queuing problem with a constant service rate, on average, how many customers are in the system?A) 1.875B) 1.125C) 0.625D) 0.375E) None of the above
Answer: A
103) According to the information provided in Table 12-4, which presents a queuing problem solution for a queuing problem with a constant service rate, on average, how many customers arrive per time period?A) 3B) 4C) 1.875D) 1.125E) None of the above
Answer: A
119) Using Table 12-6, what is the average number of customers waiting in line?A) 0.0833B) 0.5C) 0.75 D) 1.33E) 2
Answer: A
45) An arrival in a queue that reneges is one whoA) 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
Answer: A
61) A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution while service times follow an exponential distribution. If the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes, how much time will elapse (in hours) from the time a customer enters the line until he/she leaves the restaurant?A) 0.50B) 0.25C) 0.75D) 2.25E) 3.00
Answer: A
63) 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 four per minute and the average service rate of a single server is seven per minute, what is the average number of customers waiting in line behind the person being servedA) 0.76B) 0.19C) 1.33D) 1.67E) None of the above
Answer: A
68) Which of the following distributions is most often used to estimate service times?A) negative exponentialB) normalC) PoissonD) ErlangE) beta
Answer: A
85) Cars arrive at a local JLUBE franchise at the rate of 1 every 12 minutes. Service times are exponentially distributed with an average of 15 minutes. Jack Burns, the JLUBE owner, has decided to open a second work bay, i.e., make the shop into a two-channel system. Under this new scheme, the average customer will wait in lineA) approximately 9.6 minutes.B) approximately 2.5 minutes.C) approximately 24.6 minutes.D) approximately 2.1 minutes.E) None of the above
Answer: A
94) 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 be doubled.D) There is not enough information to know what will happen to the queue length and waiting time.E) None of the above
Answer: A
97) At an automatic car wash, cars arrive randomly at a rate of 7 every 30 minutes. The car wash takes exactly 4 minutes (this is constant). On average, how long would each driver have to wait before receiving service?A) 28 minutesB) 32 minutesC) 17 minutesD) 24 minutesE) None of the above
Answer: A
D) blithering.E) None of the above
Answer: A
143) What is meant by a single-phase system?
Answer: Arrivals leave the system after receiving service at only one station.
114) The school of business has 3 fax machines. The toner in each machine needs to be changed after about 5 hours of use. There is one unit secretary who is responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge. What is the average number of fax machines in the system?A) .0142 fax machineB) .1563 fax machineC) .0249 fax machineD) .2749 fax machineE) None of the above
Answer: B
48) The three major characteristics of the input source that generates arrivals or customers for the service system areA) size, demographics, and behavior.B) size, pattern, and behavior.C) demographics, pattern, and behavior.D) size, demographics, and pattern.E) None of the above
Answer: B
50) A vendor selling newspapers on a street corner is an example of aA) single-channel, multiphase system.B) single-channel, single-phase system.C) multichannel, multiphase system.D) multichannel, single-phase system.E) None of the above
Answer: B
77) A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. What proportion of time are both clerks idle?A) 0.643B) 0.250C) 0.750D) 0.143E) None of the above
Answer: B
80) Using the information provided in Table 12-1 and counting each person being served and the people in line, on average, how many people would be in this system?A) 0.521B) 1.646C) 1.125D) 0.183E) None of the above
Answer: B
83) Cars arrive at a local JLUBE franchise at the rate of 1 every 12 minutes. Service times are exponentially distributed with an average of 15 minutes. Jack Burns, the JLUBE owner, has decided to open a second work bay, i.e., make the shop into a two-channel system. Under this new scheme, the average customer will wait in an ________ line.A) M/M/1B) M/M/2C) M/D/2D) M/D/1E) M/G/2
Answer: B
87) According to the information provided in Table 12-2, which presents a queuing problem solution, on average, how many units are in the line?A) 5.455B) 3.788C) 1.091D) 0.758E) 0.833
Answer: B
96) At an automatic car wash, cars arrive randomly at a rate of 7 every 30 minutes. The car wash takes exactly 4 minutes (this is constant). On average, how long would each car spend at the car wash?A) 28 minutesB) 32 minutesC) 17 minutesD) 24 minutesE) None of the above
Answer: B
98) At an automatic car wash, cars arrive randomly at a rate of 7 every 30 minutes. The car wash takes exactly 4 minutes (this is constant). On average, how many customers would be at the car wash (waiting in line or being serviced)?A) 8.17B) 7.46C) 6.53D) 0.46E) None of the above
Answer: B
D) 2.5 minutes.E) None of the above
Answer: B
104) According to Table 12-4, which presents a queuing problem with a constant service rate, on average, how many minutes does a customer spend in the service facility?A) 0.375 minute B) 4 minutesC) 0.625 minute D) 0.25 minute E) None of the above
Answer: C
115) The school of business has 3 fax machines. The toner in each machine needs to be changed after about 5 hours of use. There is one unit secretary who is responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge. What is the average waiting time in the queue?A) .0142 hourB) .1563 hourC) .0249 hourD) .2749 hourE) None of the above
Answer: C
118) Using Table 12-6, what is the average number of customers in the coffee shop?A) 0.0833B) 0.5C) 0.75 D) 1.33E) 2
Answer: C
121) The analytic technique used to analyze complex queuing models that cannot be captured in closed-form expressions is calledA) extrapoloation.B) interpolation.C) simulation.D) linear programming.E) forecasting.
Answer: C
122) The school of business has 3 fax machines. The toner in each machine needs to be changed after about 5 hours of use. There is one unit secretary who is responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge. What is the probability that 2 fax machines need toner at the same time?A) .8576B) .1286C) .0129D) .1415E) None of the above
Answer: C
42) In queuing theory, the calling population is another name for A) the queue size.B) the servers.C) the arrivals.D) the service rate.E) the market researchers.
Answer: C
47) The customer who arrives at a bank, enters a line, and decides to leave isA) balking.B) cropping.C) reneging.D) blithering.E) None of the above
Answer: C
52) Which of the following distributions is most often used to estimate the arrival pattern?A) negative exponentialB) normalC) PoissonD) ErlangE) beta
Answer: C
59) A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution while service times follow an exponential distribution. If the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes, what is the average number of customers waiting in line behind the person being served?A) 0.50B) 0.75C) 2.25D) 3.00E) None of the above
Answer: C
60) A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution while service times follow an exponential distribution. If the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes, what proportion of the time is the server busy?A) 0.25B) 0.50C) 0.75D) 2.25E) 3.00
Answer: C
66) At a local fast-food joint, cars arrive randomly at a rate of 12 every 30 minutes. The fast food joint takes an average of 2 minutes to serve each arrival. The utilization factor for this system isA) 0.467.B) 0.547.C) 0.800.D) 0.133.E) None of the above
Answer: C
71) A queuing system with a normally distributed arrival pattern, exponential service times, and three servers would be described asA) G/G/3.B) M/M/3.C) G/M/3.D) M/G/3.E) N/E/3.
Answer: C
79) According to the information provided in Table 12-1, what proportion of time is at least one server busy?A) 0.563B) 0.437C) 0.720D) 0.280E) None of the above
Answer: C
82) According to the information provided in Table 12-1, what percentage of the total available service time is being used?A) 72.0%B) 28.0%C) 56.3%D) It could be any of the above, depending on other factors.E) None of the above
Answer: C
84) Cars arrive at a local JLUBE franchise at the rate of 1 every 12 minutes. Service times are exactly 15 minutes. Jack Burns, the JLUBE owner, has decided to open a second work bay, i.e., make the shop into a two-channel system. Under this new scheme, the average customer will wait in an ________ line.A) M/M/1B) M/M/2C) M/D/2D) M/D/1E) M/G/2
Answer: C
Customers arrive at coffee shop at a rate of 40 per hour. There are 2 servers available and it takes an average of 1 minute to serve each customer. 117) Using Table 12-6, what is the probability of no customers in the system?A) 0B) 0.333C) 0.5 D) 0.667E) 1
Answer: C
101) According to the information provided in Table 12-4, which presents a queuing problem solution for a queuing problem with a constant service rate, on average, how much time is spent waiting in line?A) 1.875 minutesB) 1.125 minutesC) 0.625 minuteD) 0.375 minuteE) None of the above
Answer: D
113) The school of business has 3 fax machines. The toner in each machine needs to be changed after about 5 hours of use. There is one unit secretary who is responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge. What is the average number of fax machines in the queue?A) 1.1658 fax machinesB) 2.9904 fax machinesC) .1563 fax machineD) .0142 fax machineE) None of the above
Answer: D
120) The school of business has 3 fax machines. The toner in each machine needs to be changed after about 5 hours of use. There is one unit secretary who is responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge. What is the average time spent in the system?A) .0142 hourB) .1563 hourC) .0249 hourD) .2749 hourE) None of the above
Answer: D
49) The term queue "discipline" describes theA) degree to which members of the queue renege.B) sequence in which members of the queue arrived.C) degree to which members of the queue are orderly and quiet.D) sequence in which members of the queue are serviced.E) All of the above
Answer: D
51) Lines at banks where customers wait for a teller window are usually representative of aA) single-channel, multiphase system.B) single-channel, single-phase system.C) multichannel, multiphase system.D) multichannel, single-phase system.E) None of the above
Answer: D
53) A single automatic car wash with one bay and a cycle time of 2.5 minutes is what type of model?A) M/M/1B) M/M/C) M/D/2D) M/D/1E) M/G/1
Answer: D
55) 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 rates follow the normal distribution.E) The average service rate is faster than the average arrival rate.
Answer: D
57) A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution, while service times follow an exponential distribution. What type of queuing model is exhibited in this problem?A) M/M/1B) M/M/2C) M/D/2D) M/D/1E) M/G/1
Answer: D
58) A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes, what is the average number of customers in the system?A) 0.50B) 4.00C) 2.25D) 3.00 E) None of the above
Answer: D
62) 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 four per minute and the average service rate of a single server is seven per minute, what is the average number of customers in the system?A) 0.43B) 1.67C) 0.57D) 1.33E) None of the above
Answer: D
65) Customers enter the waiting line to pay for food as they leave 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 four per minute and the average service rate of a single server is seven per minute, on average, how much time will elapse from the time a customer enters the line until he/she leaves the cafeteria?A) 0.67 minuteB) 0.50 minuteC) 0.75 minuteD) 0.33 minuteE) 1.33 minutes
Answer: D
67) At a local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes. Service times are random (exponential) and average 2 minutes per arrival. The average time in the queue for each arrival isA) 2 minutes.B) 4 minutes.C) 6 minutes.D) 8 minutes.E) 10 minutes.
Answer: D
70) When waiting time is based on time in the queue, which of the following is the correct equation for total cost?A) mCs + λWCwB) mCw + λWCsC) mCs + λWqCsD) mCs + λWqCwE) mCw + λWqCs
Answer: D
72) The initial state of a queuing system (for example, when a restaurant first opens), is referred to as the ________ state.A) steadyB) primaryC) introductoryD) transientE) start-up
Answer: D
76) A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. How long does the average person spend waiting for a clerk?A) 3.429 minutesB) 1.929 minutesC) 1.143 minutesD) 0.643 minuteE) None of the above
Answer: D
81) According to the information provided in Table 12-1, what is the average time spent by a person in this system?A) 0.058 minuteB) 1.646 minutesC) 0.521 minuteD) 0.183 minuteE) None of the above
Answer: D
1) Assume that we are using a waiting line model to analyze the number of service technicians required to maintain machines in a factory. Our goal should be to A) maximize productivity of the technicians. B) minimize the number of machines needing repair.C) minimize the downtime for individual machines.D) minimize the percent of idle time of the technicians.E) minimize the total cost (cost of maintenance plus cost of downtime).
Answer: E
112) Which of the following is not an assumption for the M/M/1 model with finite population source?A) There is only one server.B) The population of units seeking service are finite.C) Arrivals follow a Poisson distribution and service times are exponential.D) Customers are served on a first come, first served basis.E) The length of the queue is independent of the arrival rate.
Answer: E
41) In queuing analysis, total expected cost is the sum of expected ________ plus expected ________.A) service costs, arrival costsB) facility costs, calling costsC) calling cost, inventory costsD) calling costs, waiting costsE) service costs, waiting costs
Answer: E
44) Which of the following is not true about arrivals?A) Random arrivals are independent of each other.B) Random arrivals cannot be predicted exactly.C) The Poisson distribution is often used to represent the arrival pattern.D) Service times often follow the negative exponential distribution.E) The exponential distribution is often used to represent the arrival pattern.
Answer: E
54) A single automatic car wash with one bay and a service time that is normally distributed is what type of model?A) M/M/1B) M/M/2C) M/D/2D) M/D/1E) M/G/1
Answer: E