Asymptotic analysis of the effect of arrival model uncertainties in some optimal routing problems

Mohanty, B.P.; Cassandras, Christos G.

doi:10.1007/bf02193467

Cited by 3 publications

(1 citation statement)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Better yet, if in addition to (2) we can show that J(0) 4 0 as 8 + 8*, we will say that the design or the control policy is usyn~ptotically exact in 8. We can easily establish these properties by working Morabito, 1996; Buzacott andShanthikumar, 1992, 1993;Chen er al., 1995;Mohanty and Cassandras, 1993;Ni and Wwang, 1985;Seshadri and Pinedo, 2000;Shanthikumar, 1997;Tantawi and Towsley, 1985; Wein, 1 989; Yao and Shanthikumar, 1987). Let the holding cost rate of each customer at station i be hi, i = 1,2,. .…”

Section: Introductionmentioning

confidence: 93%

Strongly asymptotically optimal design and control of production and service systems

Shanthikumar

2000

IIE Transactions

View full text Add to dashboard Cite

In this paper we consider production and service systems that can be modeled as single or multiple stage queueing networks. We provide a formal definition of strong asymptotic optirnality in the context of design and control of such queueing systems. We describe a simple approach to obtain strongly asymptotically optimal design and control policies for these systems. We illustrate our approach through some examples. In particular we obtain a strongly asymptotically optimal workload allocation for a multiple center service system modeled by the open Jackson network. The objective here is to minimize the expected total holding cost. A simple counter example shows that the much celebrated balanced workload allocation is not even asymptotjcally optimal for minimizing the expected number of jobs in the system. We show that an index policy is strongly asymptotically optimal for the scheduling control problem in a single stage (GIGIIl) service system. We also obtain a strongly asymptotically optimal allocation of classes of customers to a multiple center service system. This allocation agrees with the traditional wisdom of forming service stations to process similar tasks that reduce fluctuations in processing times. Suggestions for further work on this topic are summarized as well.

show abstract

Section: Introductionmentioning

confidence: 93%

Strongly asymptotically optimal design and control of production and service systems

Shanthikumar

2000

IIE Transactions

View full text Add to dashboard Cite

show abstract

Effect of Modeling Uncertainty on Some Routing Problems

Kodialam

1999

Journal of Optimization Theory and Applications

View full text Add to dashboard Cite

Asymptotically Optimal Routing and Servive Rate Allocation in a Multiserver Queueing System

Shanthikumar

1997

Operations Research

View full text Add to dashboard Cite

We consider a single stage queueing system with c heterogeneous servers. Customers arrive at this system according to a renewal process with mean 1/λ and squared coefficient of variation (scv) Ca2. An incoming customer is routed to server i with probability θi, ∑i=1cθi = 1. The service times at server i are i.i.d random variables with mean 1/μi, and scv Csi2. The holding cost rate of queue i is hi per customer, i = 1, 2, …, c. The problems of interest are twofold: (a) for a fixed service rate allocation μi, ∑i=1c μi = μ, find the routing probabilities, θi*, ∑i=1c θi* = 1, that minimize the average total holding cost; and (b) for fixed routing probabilities θi, ∑i=1c θi, and total service rate μ, find the service rate allocation μi* = μδi*, ∑i=1c δi* = 1, that minimizes the average total holding cost of the system. For each problem, we characterize the optimal policy under heavy traffic conditions. We also derive the routing probabilities, θ̂i (proportions δ̂i), i = 1, …, c, that are strongly asymptotically optimal. That is, the difference between the average total holding costs under θ̂i, i = 1, …, c, and θi*, i = 1, …, c (δ̂i, i = 1, …, c, and δi*, i = 1, …, c) is bounded by a fixed constant independent of the routing probabilities (proportions) and the arrival rate. In addition, we discuss the necessity and sufficiency of the accurate knowledge of the means and scvs of the interarrival and service times m obtaining asymptotically optimal policies.

show abstract

Asymptotic analysis of the effect of arrival model uncertainties in some optimal routing problems

Cited by 3 publications

References 12 publications

Strongly asymptotically optimal design and control of production and service systems

Strongly asymptotically optimal design and control of production and service systems

Effect of Modeling Uncertainty on Some Routing Problems

Asymptotically Optimal Routing and Servive Rate Allocation in a Multiserver Queueing System

Contact Info

Product

Resources

About