Related papers: Many Server Queueing Models with Heterogeneous Ser…
This paper develops fluid limits for nonstationary many-server loss systems with general service-time distributions. For the zero-buffer $M_t/G/n/n$ queuing model, we prove a functional strong law of large numbers for the fraction of busy…
We consider a multi-hop switched network operating under a Max-Weight (MW) scheduling policy, and show that the distance between the queue length process and a fluid solution remains bounded by a constant multiple of the deviation of the…
We introduce a "system-wide safety staffing" (SWSS) parameter for multiclass multi-pool networks of any tree topology, Markovian or non-Markovian, in the Halfin-Whitt regime. This parameter can be regarded as the optimal reallocation of the…
We consider a discrete-time system comprising a first-come-first-served queue, a non-preemptive server, and a stationary non-work-conserving scheduler. New tasks enter the queue according to a Bernoulli process with a pre-specified arrival…
We consider general large-scale service systems with multiple customer classes and multiple server (agent) pools, mean service times depend both on the customer class and server pool. It is assumed that the allowed activities (routing…
Multi-server queueing systems are widely used models for job scheduling in machine learning, wireless networks, crowdsourcing, and healthcare systems. This paper considers a multi-server system with multiple servers and multiple types of…
A parallel server system with $n$ identical servers is considered. The service time distribution has a finite mean $1/\mu$, but otherwise is arbitrary. Arriving customers are be routed to one of the servers immediately upon arrival.…
A service system with multiple types of customers, arriving according to Poisson processes, is considered. The system is heterogeneous in that the servers also can be of multiple types. Each customer has an independent exponentially…
We present an analysis of large-scale load balancing systems, where the processing time distribution of tasks depends on both the task and server types. Our study focuses on the asymptotic regime, where the number of servers and task types…
We study a sequence of single server queues with customer abandonment (GI/GI/1+GI) under heavy traffic. The patience time distributions vary with the sequence, which allows for a wider scope of applications. It is known ([20, 18]) that the…
The paper studies closed queueing networks containing a server station and $k$ client stations. The server station is an infinite server queueing system, and client stations are single-server queueing systems with autonomous service, i.e.…
We consider a queue with renewal arrivals and n exponential servers in the Halfin-Whitt heavy traffic regime, where n and the arrival rate increase without bound, so that a critical loading condition holds. Server k serves at rate $\mu_k $,…
This paper obtains logarithmic asymptotics of moderate deviations of the stochastic process of the number of customers in a many--server queue with generally distributed interarrival and service times in the Halfin--Whitt heavy traffic…
We consider the problem of staffing large-scale service systems with multiple customer classes and multiple dedicated server pools under joint quality-of-service (QoS) constraints. We first analyze the case in which arrival rates are…
We consider a discrete-time parallel service system consisting of $n$ heterogeneous single server queues with infinite capacity. Jobs arrive to the system as an i.i.d. process with rate proportional to $n$, and must be immediately…
We consider a distributed cloud service deployed at a set of distinct server pools. Arriving jobs are classified into heterogeneous types, in accordance with their setup times which are differentiated at each of the pools. A dispatcher for…
We prove a many-server heavy-traffic fluid limit for an overloaded Markovian queueing system having two customer classes and two service pools, known in the call-center literature as the X model. The system uses the…
We propose a model uncertainty approach to heavy traffic asymptotics that allows for a high level of uncertainty. That is, the uncertainty classes of underlying distributions accommodate disturbances that are of order 1 at the usual…
We consider the so-called GI/GI/N queue, in which a stream of jobs with independent and identically distributed service times arrive as a renewal process to a common queue that is served by $N$ identical parallel servers in a…
We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service…