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# A group of $m$ customers frequents a single-server station in the following manner. When a customer arrives, he or she either enters service if the server is free o...

## Question

###### A group of $m$ customers frequents a single-server station in the following manner. When a customer arrives, he or she either enters service if the server is free or joins the queue otherwise. Upon completing service the customer departs the system, but then returns after an exponential time with rate $heta .$ All service times are exponentially distributed with rate $mu$.(a) Define states and set up the balance equations.In terms of the solution of the balance equations, find(b) the average rat

A group of $m$ customers frequents a single-server station in the following manner. When a customer arrives, he or she either enters service if the server is free or joins the queue otherwise. Upon completing service the customer departs the system, but then returns after an exponential time with rate $heta .$ All service times are exponentially distributed with rate $mu$. (a) Define states and set up the balance equations. In terms of the solution of the balance equations, find (b) the average rate at which customers enter the station. (c) the average time that a customer spends in the station per visit.

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