Analysis of an infinite-server queue with batch Markovian arrival streams

This paper considers an infinite-server queue with multiple batch Markovian arrival streams. The service time distribution of customers may be different for different arrival streams, and simultaneous batch arrivals from more than one stream are allowed. For this queue, we first derive a system of ordinary differential equations for the time-dependent matrix joint generating function of the number of customers in the system. Next assuming phase-type service times, we derive explicit and numerically feasible formulas for the time-dependent and limiting joint binomial moments. Further, some numerical examples are provided to discuss the impact of system parameters on the performance.