4. (25 points) There are two servers, server 1 and server 2, that serve customers with...
4. (25 points)
There are two servers, server 1 and server 2, that serve customers
with exponential service
rates 1=2 and 2=3 respectively. Customers arrive according to a
Poisson process with rate
=1. An arriving customer first enters server 1 if the server is
free. If server 1 is busy when a
customer arrives the customer leaves the system and a cost of 10 TL
is incurred. A customer
who has received service from server 1 then moves to server 2.
Similarly, if server 2 is busy
when a customer arrives then the customer departs the system and a
cost of 20 TL is incurred.
What is the average cost per unit time incurred by the system?
Homework Answers
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4. (25 points)
There are two servers, server 1 and server 2, that serve customers
with...
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2. [3] Suppose you arrive to a service system with three parallel servers. All servers are busy, and there is no customer ahead of you in the queue. As soon as one of the servers is free, you will be served by that server. Service times at each server are exponentially distributed with rates 1, 2, and us. What is the expected time you will spend in the system?
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2. [3] Suppose you arrive to a service system with three parallel servers. All servers are busy, and there is no customer ahead of you in the queue. As soon as one of the servers is free, you will be served by that server. Service times at each server are exponentially distributed with rates 1, 2, and us. What is the expected time you will spend in the system?
2. [3] Suppose you arrive to a service system with three...
Problem 3 (25pts) A group of n customers moves around among two servers. Upon completion of service, the served customer then joins the queue (or enters service if the server is free) at the other server. All service times are exponential with rate μ. Find the proportion of time that there are j customers at server 1, j- 0, .,n.
Problem 3 (25pts) A group of n customers moves around among two servers. Upon completion of service, the served customer...
2. (3) Suppose you arrive to a service system with three parallel servers. All servers are basy, and there is no customer ahead of you in the queue. As soon as one of the servers is free, you will be served by that server. Service times at each server are exponentially distributed with rates μ1,P2, and μ3, what is the expected time you will spend in the system?
2. (3) Suppose you arrive to a service system with three parallel...
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Problem 4. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive ac cording to a Poisson process at a mean rate of 4 per minute. However, business is growing and management projects that the mean arrival rate will be 6 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 0.5 minute. Management has established the following guidelines for a satis- factory level...
Consider a two-server system in which a customer is served first by server 1, then by server 2, and then leaves. The service time at server 1 is exponentially distributed with mean 15 minutes, the service time at server 2 is exponentially distributed with mean 10 minutes, and all service times are independent. When Alex arrives, he finds that Bob is currently with server 1, and Carl is currently with server 2. Find Alex's expected total time in the system...
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