Reward Processes and Performance Simulation in Supermarket Models with Different Servers

TL;DR

This paper introduces a novel analytical method using multi-dimensional continuous-time Markov reward processes to evaluate reward-based performance metrics in supermarket models with diverse servers, aiding resource management analysis.

Contribution

It develops a new approach employing Markov reward processes and event-driven techniques to analyze supermarket models with different servers, including computation of expected rewards over finite and infinite periods.

Findings

Expected queue lengths depend on main model parameters.

The method effectively computes mean rewards in finite and infinite time.

Simulation results illustrate the impact of server heterogeneity.

Abstract

Supermarket models with different servers become a key in modeling resource management of stochastic networks, such as, computer networks, manufacturing systems and transportation networks. While these different servers always make analysis of such a supermarket model more interesting, difficult and challenging. This paper provides a new novel method for analyzing the supermarket model with different servers through a multi-dimensional continuous-time Markov reward processes. Firstly, the utility functions are constructed for expressing a routine selection mechanism that depends on queue lengths, on service rates, and on some probabilities of individual preference. Then applying the continuous-time Markov reward processes, some segmented stochastic integrals of the random reward function are established by means of an event-driven technique. Based on this, the mean of the random reward function in a finite time period is effectively computed by means of the state jump points of the Markov reward process, and also the mean of the discounted random reward function in an infinite time period can be calculated through the same event-driven technique. Finally, some simulation experiments are given to indicate how the expected queue length of each server depends on the main parameters of this supermarket model.