수 25 5월 2016

Q. Consider \(M/M/1\) system with arrival rate \(\lambda\) and service rate \(\mu\). The customer getting out of the server leaves the system with probability \(q\) or again enters the server for additional service with probability \((1-q)\).

(a) Derive the probability that \(k\) customers are in the system, denoted by \(P_k\).

(b) Derive the mean number of customers in the system, \(N\), and the mean sojourn time of a customer in the system, \(T\).

A.

Category: quiz Tagged: system analysis quiz markov chain transition probability diagram