TY - JOUR
T1 - Heavy-traffic limits for a many-server queueing network with switchover
AU - Pang, Guodong
AU - Yao, David D.
N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2013/9
Y1 - 2013/9
N2 - We study a multiclass Markovian queueing network with switchover across a set of many-server stations. New arrivals to each station follow a nonstationary Poisson process. Each job waiting in queue may, after some exponentially distributed patience time, switch over to another station or leave the network following a probabilistic and state-dependent mechanism. We analyze the performance of such networks under the many-server heavy-traffic limiting regimes, including the critically loaded quality-andefficiency- driven (QED) regime, and the overloaded efficiency-driven (ED) regime. We also study the limits corresponding to mixing the underloaded quality-driven (QD) regime with the QED and ED regimes. We establish fluid and diffusion limits of the queuelength processes in all regimes. The fluid limits are characterized by ordinary differential equations. The diffusion limits are characterized by stochastic differential equations, with a piecewise-linear drift term and a constant (QED) or time-varying (ED) covariance matrix. We investigate the load balancing effect of switchover in the mixed regimes, demonstrating the migration ofworkload from overloaded stations to underloaded stations and quantifying the load balancing impact of switchover probabilities.
AB - We study a multiclass Markovian queueing network with switchover across a set of many-server stations. New arrivals to each station follow a nonstationary Poisson process. Each job waiting in queue may, after some exponentially distributed patience time, switch over to another station or leave the network following a probabilistic and state-dependent mechanism. We analyze the performance of such networks under the many-server heavy-traffic limiting regimes, including the critically loaded quality-andefficiency- driven (QED) regime, and the overloaded efficiency-driven (ED) regime. We also study the limits corresponding to mixing the underloaded quality-driven (QD) regime with the QED and ED regimes. We establish fluid and diffusion limits of the queuelength processes in all regimes. The fluid limits are characterized by ordinary differential equations. The diffusion limits are characterized by stochastic differential equations, with a piecewise-linear drift term and a constant (QED) or time-varying (ED) covariance matrix. We investigate the load balancing effect of switchover in the mixed regimes, demonstrating the migration ofworkload from overloaded stations to underloaded stations and quantifying the load balancing impact of switchover probabilities.
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U2 - 10.1239/aap/1377868533
DO - 10.1239/aap/1377868533
M3 - Article
AN - SCOPUS:84885014652
SN - 0001-8678
VL - 45
SP - 645
EP - 672
JO - Advances in Applied Probability
JF - Advances in Applied Probability
IS - 3
ER -