Product-Form Solutions for Integrated Services Packet Networks and Cloud Computing Systems

Wanyang Dai

doi:10.1155/2014/767651

Abstract

We iteratively derive the product-form solutions of stationary distributions for a type of preemptive priority multiclass queueing networks with multiserver stations. This type of queueing systems can typically be used to model the stochastic dynamics of some large scale backbone networks with multiprocessor shared-memory switches or local (edge) cloud computing centers with parallel-server pools. The queueing networks are Markovian with exponential interarrival and service time distributions. The obtained iterative solutions can be used to conduct performance analysis or as comparison criteria for approximation and simulation studies. Numerical comparisons with existing Brownian approximating model (BAM) related to general interarrival and service times are provided to show the effectiveness of our current designed algorithm and our previous derived BAM. Furthermore, based on the iterative solutions, we can also give some analysis concerning network stability for some cases of these queueing systems, which provides some insight for more general study.

Highlights

At present, integrated services packet networks (ISPN) are widely used to transport a wide range of information such as voice, video, and data
We iteratively derive the product-form solutions of stationary distributions for a type of preemptive priority multiclass queueing networks with multiserver stations. This type of queueing systems can typically be used to model the stochastic dynamics of some large scale backbone networks with multiprocessor shared-memory switches or local cloud computing centers with parallelserver pools
Based on the iterative solutions, we can give some analysis concerning network stability for some cases of these queueing systems, which provides some insight for more general study

Summary

Introduction

At present, integrated services packet networks (ISPN) are widely used to transport a wide range of information such as voice, video, and data. Note that the stochastic dynamics of the backbone networks with multiprocessor shared-memory switches and the local (edge) cloud computing centers with parallel-server pools in Figure 1 can both be described by a multiclass queueing networks with parallel servers at each station. Under a general Whittle network framework, the product-form solutions are presented in Serfozo [16] for some multiclass networks, which include those with sectordependent (e.g., Example 3.3) and class-station-dependent service rates (e.g., BCMP networks, which are introduced by Baskett et al [17]). In this paper, we use the method of solving Kolmogorov (balance) equations to get the product-form solutions iteratively, which are more engineering and computationally friendly By this method, we can give some analysis concerning network stability for some cases of these systems, which provides some insight for more general study.

The Queueing Network Model

Steady-State Queue Length Distributions

Numerical Comparisons

Proofs of Theorem 1 and Proposition 2

Proof of Proposition 2

Conclusion