Admission controls for Erlang's loss system with service times distributed as a finite sum of exponential random variables

Brian Moretta,Ilze Ziedins

doi:10.1155/s1173912698000066

Abstract

It is known that a threshold policy (or trunk reservation policy) is optimal for Erlang’s loss system under certain assumptions. In this paper we examine the robustness of this policy under departures from the standard assumption of exponential service times (call holding times) and give examples where the optimal policy has a generalized trunk reservation form.

Highlights

We consider a single link loss network consisting of C circuits or servers, each able to carry a single call or customer
We can think of the service time for a customer as being the time it takes for a Markov process to move from states 1 through to I and to leave state I, assuming that when the process leaves state it must move to i + 1, and that the time it spends in state is exponentially distributed with mean 1/#
We review briefly the theory of Markov and semi-Markov decision processes as it applies to this problem

Summary

Introduction

We consider a single link loss network consisting of C circuits or servers, each able to carry a single call or customer. The single link has been examined by Ziedins[33], who considered the form of the optimal policy when interarrival times are distributed as a sum of exponentials She found that a generalized trunk reservation policy, closely related to that of the examples given by us below, is optimal. Jo and Stidham[ll] found policies for the control of service rates in an MIGI1 queue In both cases results were first shown for phase-type distributions and extended to general distributions. It is known that the equilibrium distribution for an MIGICIC queue is insensitive to the form of the holding time distribution and depends on it only through its mean (see for example Burman, Lehoczky and Lim[3]) We show that this insensitivity still holds when simple trunk reservation controls (not of the generalized kind) are applied.

Markov decision theory

Structure of optimal policies and monotonicity

Trunk reservation and numerical examples

Findings

Concluding Remarks