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Problem 1. Consider a telephone system with three lines. Calls arrive according to a Poisson process...
An airline ticket office has two ticket agents answering incoming phone calls for flight reservations. In...
An airline ticket office has two ticket agents answering incoming phone calls for flight reservations. In addition, one caller can be put on "hold" until one of the agents is available to take the call. If all three phone lines (both agent lines and the hold lines) are busy, a potential customer gets a busy signal, and it is assumed she calls another ticket office, so that her business is lost. The calls and attempted calls occur randomly i.e., according...
Consider the call center model with 8 agents and ability to put at most 4 callers...
Consider the call center model with 8 agents and ability to put at most 4 callers on hold. Calls arrive according to a Poisson process with rate 60 calls per hour. Call handling times are i.i.d. exponential random variables with mean 6 minutes. Any call that arrives when all agents are busy and 4 callers are on hold, is lost. What is the expected time when all agents are busy in an 8-hour shift? Assume none of the agents is...
Problem 5 Consider the call center model with 8 agents and ability to put at most 4 callers on ho...
Problem 5 Consider the call center model with 8 agents and ability to put at most 4 callers on hold. Calls arrive according to a Poisson process with rate 60 calls per hour. Call handling times are i.i.d. expo- nential random variables with mean 6 minutes. Any call that arrives when all agents are busy and 4 callers are on hold, is lost. What is the expected time when all agents are busy in an 8-hour shift? Assume none of...
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...
Problem 4. Marsha operates an expresso stand. Customers arrive according to a Poisson process at ...
Problem 4. Marsha operates an expresso stand. Customers arrive according to a Poisson process at a mean rate of 30 per hour. The time needed by Marsha to serve a customer has an exponential distribution with a mean of 90 seconds (a) Find L, Lq, W, and W (b) Suppose Marsha is replaced by an expresso vending machine that requires exactly 75 seconds for each customer to operate. Find L, Lq, W, and W
Problem 4. Marsha operates an expresso...
Messages arrive to a computer server according to a Poisson distribution with a mean rate of...
Messages arrive to a computer server according to a Poisson distribution with a mean rate of 10messages per hour. a) What is the probability that hte first message arrives in the first 5 minutes? (randome variable time) b) What is the probability that 3 messages arrive in 20 minutes? (random variable # of messages)
Problem 2. Customers arrive at a call center according to a Poisson process with rate 6/....
Problem 2. Customers arrive at a call center according to a Poisson process with rate 6/. (a) Find the probability that the 5th call comes within 10 minutes of the 4th call. (b) Find the probability that the 9th call comes within 15 minutes of the 7th call.
Messages arrive to a computer server according to a Poisson distribution with a mean rate of...
Messages arrive to a computer server according to a Poisson distribution with a mean rate of 10 per hour. Round your answers to four decimal places (e.g. 98.7654). (a) What is the probability that 9 messages will arrive in 2 hours? (b) What is the probability that 10 messages arrive in 75 minutes?
2. Suppose buses arrive at a bus stop according to an approximate Poisson process at a...
2. Suppose buses arrive at a bus stop according to an approximate Poisson process at a mean rate of 4 per hour (60 minutes). Let Y denote the waiting time in minutes until the first bus arrives. (a) (5 points) What is the probability density function of Y? (b) (5 points) Suppose you arrive at the bus stop. What is the probability that you have to wait less than 5 minutes for the first bus? (c) (5 points) Suppose 10...
Suppose that mechanics arrive randomly at a tool crib according to a Poisson process with rate...
Suppose that mechanics arrive randomly at a tool crib according to a Poisson process with rate 1 = 10 per hour. It is known that the single tool clerk serves a mechanic in 4 minutes on the average, with a standard deviation of approximately 2 minutes. Suppose that mechanics make $15.00 per hour. Estimate the steady-state average cost per hour of mechanics waiting for tools.
An airline ticket office has two ticket agents answering incoming phone calls for flight reservations. In addition, one caller can be put on "hold" until one of the agents is available to take the call. If all three phone lines (both agent lines and the hold lines) are busy, a potential customer gets a busy signal, and it is assumed she calls another ticket office, so that her business is lost. The calls and attempted calls occur randomly i.e., according...
Problem 5 Consider the call center model with 8 agents and ability to put at most 4 callers on hold. Calls arrive according to a Poisson process with rate 60 calls per hour. Call handling times are i.i.d. expo- nential random variables with mean 6 minutes. Any call that arrives when all agents are busy and 4 callers are on hold, is lost. What is the expected time when all agents are busy in an 8-hour shift? Assume none of...
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...
Problem 4. Marsha operates an expresso stand. Customers arrive according to a Poisson process at a mean rate of 30 per hour. The time needed by Marsha to serve a customer has an exponential distribution with a mean of 90 seconds (a) Find L, Lq, W, and W (b) Suppose Marsha is replaced by an expresso vending machine that requires exactly 75 seconds for each customer to operate. Find L, Lq, W, and W
Problem 4. Marsha operates an expresso...
Problem 2. Customers arrive at a call center according to a Poisson process with rate 6/. (a) Find the probability that the 5th call comes within 10 minutes of the 4th call. (b) Find the probability that the 9th call comes within 15 minutes of the 7th call.
2. Suppose buses arrive at a bus stop according to an approximate Poisson process at a mean rate of 4 per hour (60 minutes). Let Y denote the waiting time in minutes until the first bus arrives. (a) (5 points) What is the probability density function of Y? (b) (5 points) Suppose you arrive at the bus stop. What is the probability that you have to wait less than 5 minutes for the first bus? (c) (5 points) Suppose 10...
Suppose that mechanics arrive randomly at a tool crib according to a Poisson process with rate 1 = 10 per hour. It is known that the single tool clerk serves a mechanic in 4 minutes on the average, with a standard deviation of approximately 2 minutes. Suppose that mechanics make $15.00 per hour. Estimate the steady-state average cost per hour of mechanics waiting for tools.
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