M/M/1 Differentiated Multiple Vacation Queueing Systems with Vacation-Dependent Service Rates
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We consider a multiple vacation queueing system in which a vacation following a busy period has a different distribution from a vacation that is taken without serving at least one customer. In addition, the service rate after a vacation taken after a busy period of non-zero duration is different from that of a vacation taken after a busy period of zero duration. This is in keeping with real life experience where the rate at which someone is serving might depend on how much rest he/she had before working. For ease of analysis it is assumed that the service times are exponentially distributed with different means, and the two vacation types are also exponentially distributed but with different means. The steady-state solution of the model is obtained.
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