TY - JOUR
T1 - Infinite horizon asymptotic average optimality for large-scale parallel server networks
AU - Arapostathis, Ari
AU - Pang, Guodong
N1 - Funding Information:
This research was supported in part by the Army Research Office through grant W911NF-17-1-0019 , and in part by the National Science Foundation through grants DMS-1715210 and DMS-1715875 . In addition, the work of Ari Arapostathis was supported in part by the Office of Naval Research through grant N00014-16-1-2956 .
Publisher Copyright:
© 2018
PY - 2019/1
Y1 - 2019/1
N2 - We study infinite-horizon asymptotic average optimality for parallel server networks with multiple classes of jobs and multiple server pools in the Halfin–Whitt regime. Three control formulations are considered: (1) minimizing the queueing and idleness cost, (2) minimizing the queueing cost under constraints on idleness at each server pool, and (3) fairly allocating the idle servers among different server pools. For the third problem, we consider a class of bounded-queue, bounded-state (BQBS) stable networks, in which any moment of the state is bounded by that of the queue only (for both the limiting diffusion and diffusion-scaled state processes). We show that the optimal values for the diffusion-scaled state processes converge to the corresponding values of the ergodic control problems for the limiting diffusion. We present a family of state-dependent Markov balanced saturation policies (BSPs) that stabilize the controlled diffusion-scaled state processes. It is shown that under these policies, the diffusion-scaled state process is exponentially ergodic, provided that at least one class of jobs has a positive abandonment rate. We also establish useful moment bounds, and study the ergodic properties of the diffusion-scaled state processes, which play a crucial role in proving the asymptotic optimality.
AB - We study infinite-horizon asymptotic average optimality for parallel server networks with multiple classes of jobs and multiple server pools in the Halfin–Whitt regime. Three control formulations are considered: (1) minimizing the queueing and idleness cost, (2) minimizing the queueing cost under constraints on idleness at each server pool, and (3) fairly allocating the idle servers among different server pools. For the third problem, we consider a class of bounded-queue, bounded-state (BQBS) stable networks, in which any moment of the state is bounded by that of the queue only (for both the limiting diffusion and diffusion-scaled state processes). We show that the optimal values for the diffusion-scaled state processes converge to the corresponding values of the ergodic control problems for the limiting diffusion. We present a family of state-dependent Markov balanced saturation policies (BSPs) that stabilize the controlled diffusion-scaled state processes. It is shown that under these policies, the diffusion-scaled state process is exponentially ergodic, provided that at least one class of jobs has a positive abandonment rate. We also establish useful moment bounds, and study the ergodic properties of the diffusion-scaled state processes, which play a crucial role in proving the asymptotic optimality.
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U2 - 10.1016/j.spa.2018.03.005
DO - 10.1016/j.spa.2018.03.005
M3 - Article
AN - SCOPUS:85044271922
SN - 0304-4149
VL - 129
SP - 283
EP - 322
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 1
ER -