Question: For an M/M/1 queueing system with Poisson arrival with rateand exponential service time with mean 1/(rate), some customers may bedissatisfiedwith the service they received and

For an M/M/1 queueing system with Poisson arrival with rateand exponential service time with mean 1/(rate), some customers may bedissatisfiedwith the service they received and must be served again. Suppose that on completion of service, a customer is dissatisfied with probability 1, for some 0< <1,independently ofwhether that customer had been dissatisfied (one or more times) before. If customers are always satisfied (i.e., if= 1), we have a standard M/M/1 system. See Figure 1 below for illustration. Subsequent service times on the same customer, if any, are also independent and exponentially distributed with mean 1/. Assume that dissatisfied customers are served again immediately in the server, until satisfied.

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