Designing a Call Center with Impatient Customers
Manufacturing & Service Operations Management
Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects
Manufacturing & Service Operations Management
Heavy Traffic Limits for Queues with Many Deterministic Servers
Queueing Systems: Theory and Applications
Queues with Many Servers: The Virtual Waiting-Time Process in the QED Regime
Mathematics of Operations Research
Stationary Distribution Convergence for Generalized Jackson Networks in Heavy Traffic
Mathematics of Operations Research
Queueing Systems: Theory and Applications
Control of systems with flexible multi-server pools: a shadow routing approach
Queueing Systems: Theory and Applications
Queues with Many Servers and Impatient Customers
Mathematics of Operations Research
A large-scale service system with packing constraints: minimizing the number of occupied servers
Proceedings of the ACM SIGMETRICS/international conference on Measurement and modeling of computer systems
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We consider a heterogeneous queueing system consisting of one large pool of O(r) identical servers, where r驴驴 is the scaling parameter. The arriving customers belong to one of several classes which determines the service times in the distributional sense. The system is heavily loaded in the Halfin---Whitt sense, namely the nominal utilization is $1-a/\sqrt{r}$ where a0 is the spare capacity parameter. Our goal is to obtain bounds on the steady state performance metrics such as the number of customers waiting in the queue Q r (驴). While there is a rich literature on deriving process level (transient) scaling limits for such systems, the results for steady state are primarily limited to the single class case.This paper is the first one to address the case of heterogeneity in the steady state regime. Moreover, our results hold for any service policy which does not admit server idling when there are customers waiting in the queue. We assume that the interarrival and service times have exponential distribution, and that customers of each class may abandon while waiting in the queue at a certain rate (which may be zero). We obtain upper bounds of the form $O(\sqrt{r})$ on both Q r (驴) and the number of idle servers. The bounds are uniform w.r.t. parameter r and the service policy. In particular, we show that $\limsup_{r} \mathbb {E}\exp(\theta r^{-{1\over2}}Q^{r}(\infty)) . Therefore, the sequence $r^{-{1\over2}}Q^{r}(\infty)$ is tight and has a uniform exponential tail bound. We further consider the system with strictly positive abandonment rates, and show that in this case every weak limit $\hat{Q}(\infty)$ of $r^{-{1\over2}}Q^{r}(\infty)$ has a sub-Gaussian tail. Namely, $\mathbb {E}[\exp(\theta(\hat{Q}(\infty ))^{2})] , for some 驴0.