Queues with Nonexponential Failure Times

There are two difficulties with the inclusion of nonexponential failure times in queueing models. The first effect is that the failures will change the mean and variance (as well as higher moments) of the effective service times. The second difficulty is less obvious in that nonexponential failures will eliminate the stochastic independence between successive service times. Using phase-type distributions to model failure and repair times, it is relatively simple to model an M/M/1 queueing systems with failures; however, the “curse of dimensionality" takes over for G/G/1 systems with failures. Therefore, we propose in this paper to use an M/M/1 model with server failures as the basis for an approximation to more general systems.