Analysis of Discrete-Time Queues with Branching Arrivals

Abstract

We consider a discrete-time single server queueing system, where arrivals stem from a multi-type Galton–Watson branching process with migration. This branching-type arrival process exhibits intricate correlation, and the performance of the corresponding queueing process can be assessed analytically. We find closed-form expressions for various moments of both the queue content and packet delay. Close inspection of the arrival process at hand, however, reveals that sample paths consist of large independent bursts of arrivals followed by geometrically distributed periods without arrivals. Allowing for non-geometric periods without arrivals, and correlated bursts, we apply π-thinning on the arrival process. As no closed-form expressions can be obtained for the performance of the corresponding queueing system, we focus on approximations of the main performance measures in the light and heavy traffic regimes.

Keywords

• discrete-time queue
• arrival correlation
• branching process