Combined Analysis of Transient Delay Characteristics and Delay Autocorrelation Function in the Geo^X/G/1 Queue

Abstract

We perform a discrete-time analysis of customer delay in a buffer with batch arrivals. The delay of the kth customer that enters the FIFO buffer is characterized under the assumption that the numbers of arrivals per slot are independent and identically distributed. By using supplementary variables and generating functions, z-transforms of the transient delays are calculated. Numerical inversion of these transforms lead to results for the moments of the delay of the kth customer. For computational reasons k cannot be too large. Therefore, these numerical inversion results are complemented by explicit analytic expressions for the asymptotics for large k. We further show how the results allow us to characterize jitter-related variables, such as the autocorrelation of the delay in steady state.

Keywords:

• Autocorrelation
• Delay
• Generating functions
• Transient analysis

Mathematics Subject Classification:

• Primary 60K25
• Secondary 90B22

ACKNOWLEDGMENT

The first two authors are Postdoctoral Fellows with the Research Foundation, Flanders (F. W. O.-Vlaanderen), Belgium.