1) Find the probability that there are no customers in the system, given that: (i) number...
1) Find the probability that there are no customers in the
system, given that:
(i) number of channels in parallel = 3
(ii) mean arrival rate = 24 per hour
(iii) mean service rate of each channel = 10 per hour
Homework Answers
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1) Find the probability that there are no customers in the
system, given that:
(i) number...
Example 1 Follow National Bank FNB operates a drive-up teller window that allows customers to complete...
Example 1 Follow National Bank FNB operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings cars arrive randomly with a mean arrival rate of 24 customers per hour (0.4 per minute) What is the expected number of customers that will arrive in a 5-minute period? Delays are expected if more than 3 customers arrive during any 5-minute period. What is the probability that delays will occur? Assume that...
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Roblem Consider a single server queueing system where the customers arrive according to a Poisson...
roblem Consider a single server queueing system where the customers arrive according to a Poisson process with a mean rate of 18 per hour, and the service time follows an exponential distribution with a mean of 3 minutes. (1). What is the probability that there are more than 3 customers in the system? (2). Compute L, Lq and L, (3). Compute W, W and W (4). Suppose that the mean arrival rate is 21 instead of 18, what is the...
A fast food franchise is considering a drive-up window food-service operation. Assume that customer arrivals follow...
A fast food franchise is considering a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution with a mean arrival rate of 24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive up to the service window to pay for and receive their order. The following three service alternatives are being considered: a) A single-channel...
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QUESTION 8 Oakland post office uses a multiple channel queue, where customers wait in a single line for the first available window. The average service time is 1 minute per cust, and the arrival rate is 1.4 cust. per minute, and # of channels, S-2 True/False PO Probability zero customers in the system between 0.17 and 0.18 True False
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Consider the M/M/1/GD/∞/∞ queuing system where λ and μ are the arrival and server rate, respectively. Suppose customers arrive according to a rate given by λ = 12 customers per hour and that service time is exponential with a mean equal to 3 minutes. Suppose the arrival rate is increased by 20%. Determine the change in the average number of customers in the system and the average time a customer spends in the system.
A discouraging M/M/1 queue behaves as M/M/1 but with an arrival rate equal to l/(j+1), where j is the number of customers in the system. a) Find the probability of each state. b) What is the average n...
A discouraging M/M/1 queue behaves as M/M/1 but with an arrival rate equal to l/(j+1), where j is the number of customers in the system. a) Find the probability of each state. b) What is the average number of customers in the system?
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3. For a single-server, single-line, single-phase waiting line system, where l represents the mean arrival rate of customers and m represents the mean service rate, what is the formula for the average utilization of the system? a) l / m b) l / (m-l) c) l2 / m(m-l) d) 1 / (m-l) e) l / m(m-l) 4. For a single-server, single-line, single-phase waiting line system, where l represents the mean arrival rate of customers and m represents the mean service...
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**LOOKING FOR FORMULAS, ANSWERS PROVIDED. Problem-1: At a single-phase, multiple-channel service facility, customers arrive randomly. Statistical analysis of past data shows that the interarrival time has a mean of 20 minutes and a standard deviation of 4 minutes. The service time per customer has a mean of 15 minutes and a standard deviation of 5 minutes. The waiting cost is $200 per customer per hour. The server cost is $25 per server per hour. Assume general probability distribution and no...
A street noodle vendor in Singapore can service an average of 10 customers per hour. Given...
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Example 1 Follow National Bank FNB operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings cars arrive randomly with a mean arrival rate of 24 customers per hour (0.4 per minute) What is the expected number of customers that will arrive in a 5-minute period? Delays are expected if more than 3 customers arrive during any 5-minute period. What is the probability that delays will occur? Assume that...
roblem Consider a single server queueing system where the customers arrive according to a Poisson process with a mean rate of 18 per hour, and the service time follows an exponential distribution with a mean of 3 minutes. (1). What is the probability that there are more than 3 customers in the system? (2). Compute L, Lq and L, (3). Compute W, W and W (4). Suppose that the mean arrival rate is 21 instead of 18, what is the...
QUESTION 8 Oakland post office uses a multiple channel queue, where customers wait in a single line for the first available window. The average service time is 1 minute per cust, and the arrival rate is 1.4 cust. per minute, and # of channels, S-2 True/False PO Probability zero customers in the system between 0.17 and 0.18 True False
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