Exact distribution of discrete-time D-BMAP/G/\inf queueing model

TL;DR

This paper derives the exact time-dependent distribution and moments for a discrete-time D-BMAP/G/∞ queueing model using Markovian dynamics, verified by simulations, and compares it with continuous-time models.

Contribution

It introduces a method to obtain exact distributions for the discrete-time D-BMAP/G/∞ queue, filling a gap in queueing theory analysis.

Findings

Exact distribution and moments derived for the queue model

Numerical verification confirms theoretical results

Comparison with continuous-time models highlights differences

Abstract

In this paper, we consider discrete-time D-BMAP/G/\inf queueing model. We construct effective discrete-time Markovian dynamics for this model and utilize it to derive exact time-dependent distribution of customer number and the corresponding moments for the original queueing model. Numerical simulations are used to verify our results. Using our result, we provide analytical distribution for discrete-time M/M/\inf, and then compare it with the distribution of continuous-time M/M/\inf.