Abstract
An M/M/m queue with mixed loss and delay calls was analyzed by J. W. Cohen half a century ago (1956) where the two types of calls had identical constant arrival and service rates. It is straightforward to extend his analysis to an M/M/m/K queue. In this chapter, we further generalize the model such that the call arrival rates can depend on the number of calls present in the system at the arrival time. This model includes the balking and the finite population size models as special cases. We present a method of calculating the blocking probability for loss calls as well as the distribution of the waiting time for accepted delay calls. We solve a set of linear simultaneous equations for the state probabilities by numerical computation. The effects of loss calls on the mean waiting time of delayed calls are discussed based on the numerical results.
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