Related papers: Diffusion limits for shortest remaining processing…
This paper studies the effect of an overdispersed arrival process on the performance of an infinite-server system. In our setup, a random environment is modeled by drawing an arrival rate $\Lambda$ from a given distribution every $\Delta$…
In a network, arrival process is converted into departure process through network elements. The departure process suffer propagation delay in the link, processing delay at the network elements like router and data loss due to buffer…
In this paper we analyze a single server queue with batch arrivals and semi-Markovian service times. We also include the feature that the first service of each busy period might have a different distribution than subsequent service times.…
We study a single server FIFO queue that offers general service. Each of n customers enter the queue at random time epochs that are inde- pendent and identically distributed. We call this the random scattering traffic model, and the…
We study a single server queue under a processor-sharing type of scheduling policy, where the weights for determining the sharing are given by functions of each job's remaining service(processing) amount, and obtain a fluid limit for the…
This paper studies the heavy-traffic joint distribution of queue lengths in two stochastic processing networks (SPN), viz., an input-queued switch operating under the MaxWeight scheduling policy and a two-server parallel server system…
We study the information traffic in Barab\'asi-Albert scale free networks wherein each node has finite queue length to store the packets. It is found that in the case of shortest path routing strategy the networks undergo a first order…
This work considers a many-server queueing system in which customers with i.i.d., generally distributed service times enter service in the order of arrival. The dynamics of the system is represented in terms of a process that describes the…
We consider a system of parallel queues where tasks are assigned (dispatched) to one of the available servers upon arrival. The dispatching decision is based on the full state information, i.e., on the sizes of the new and existing jobs. We…
We consider a single server retrial queue with the server subject to interruptions and classical retrial policy for the access from the orbit to the server. We analyze the equilibrium distribution of the system and obtain the generating…
We study a queueing network with a single shared server, that serves the queues in a cyclic order according to the gated service discipline. External customers arrive at the queues according to independent Poisson processes. After…
The focus of this paper is on the asymptotics of large-time numbers of customers in time-periodic Markovian many-server queues with customer abandonment in heavy traffic. Limit theorems are obtained for the periodic number-of-customers…
We study the infinite horizon optimal control problem for N-network queueing systems, which consist of two customer classes and two server pools, under average (ergodic) criteria in the Halfin-Whitt regime. We consider three control…
The paper considers a queueing system with limited processor sharing. No more than n jobs may be served simultaneously. This system may be used for modeling bandwidth sharing in wireless communication systems and processes of service in…
There is a growing interest in development of in-network dispersed computing paradigms that leverage the computing capabilities of heterogeneous resources dispersed across the network for processing massive amount of data is collected at…
This is an expository review paper illustrating the ``martingale method'' for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximations. Careful treatment is given to an…
In this work, we study the stationary distribution of the scaled queue length vector process in multiclass queueing networks operating under static buffer priority service policies. We establish that when subjected to a multi-scale heavy…
We study multiclass many-server queues for which the arrival, service and abandonment rates are all modulated by a common finite-state Markov process. We assume that the system operates in the "averaged" Halfin-Whitt regime, which means…
We study a stochastic network that consists of a set of servers processing multiple classes of jobs. Each class of jobs requires a concurrent occupancy of several servers while being processed, and each server is shared among the job…
We consider the problem of preemptively scheduling jobs to minimize mean response time of an M/G/1 queue. When we know each job's size, the shortest remaining processing time (SRPT) policy is optimal. Unfortunately, in many settings we do…