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Heavy-Traffic Analysis of Queueing Systems with No Complete Resource Pooling

We study the heavy-traffic limit of the generalized switch operating under MaxWeight, without assuming that the complete resource pooling condition is satisfied and allowing for correlated arrivals. The main contribution of this paper is the steady-state mean of linear combinations of queue lengths in heavy traffic. We showcase the generality of our result by presenting various stochastic networks as corollaries, each of which is a contribution by itself. In particular, we study the input-queued switch with correlated arrivals, and we show that, if the state space collapses to a full-dimensional subspace, the correlation among the arrival processes does not matter in heavy traffic. We exemplify this last case with a parallel-server system, an N-system, and an ad hoc wireless network. Whereas these results are obtained using the drift method, we additionally present a negative result showing a limitation of the drift method. We show that it is not possible to obtain the individual queue lengths using the drift method with polynomial test functions. We do this by presenting an alternate view of the drift method in terms of a system of linear equations, and we use this system of equations to obtain bounds on arbitrary linear combinations of the queue lengths.

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Informasi Detail

Judul Seri

MATHEMATICS OF OPERATIONS RESEARCH; Vol.47 No.4 November 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 3129-3155

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

STATE-SPACE COLLAPSE
INPUT-QUEUED SWITCH
DRIFT METHOD
GENERALIZED SWITCH
N-SYSTEM

Info Detail Spesifik

https://doi.org/10.1287/moor.2021.1248

Pernyataan Tanggungjawab

Daniela Andrea Hurtado Lange, Siva Theja Maguluri

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