Some Results for Hyper-Exponential and Hyper-Poisson Queues

Authors

Shailesh J. Mehta
S. Subba Rao

Document Type

Report

Publication Date

8-1-1973

Abstract

This paper examines steady-state queuing systems, focusing on hyper-exponential and hyper-Poisson queues. Explicit queue length probabilities, waiting time distributions, and related metrics are derived using an imbedded Markov chain technique for M|HE₂|1, HE₂|M|1, and M|HEₙ|1 systems. The analysis addresses stochastic service rates with multi-point distributions, providing solutions for busy period distributions in specific queuing models. A cubic equation for the Laplace transform of the busy period distribution is also presented, offering a detailed approach to understanding queue dynamics and performance metrics.

Keywords

Operations research, Queuing theory, Markov processes, Laplace transformation

Publication Title

Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University

Issue

Technical memorandum no. 311

Rights

This work is in the public domain and may be freely downloaded for personal or academic use

Recommended Citation

Mehta, Shailesh J. and Subba Rao, S., "Some Results for Hyper-Exponential and Hyper-Poisson Queues" (1973). Research Reports from the Department of Operations. 546.
https://commons.case.edu/wsom-ops-reports/546