Related papers: Heavy Traffic Limit for a Tandem Queue with Identi…
We consider the steady-state distribution of the sojourn time of a job entering an M/GI/1 queue with the foreground-background scheduling policy in heavy traffic. The growth rate of its mean, as well as the limiting distribution, are…
In this paper we study a non-stationary Markovian queueing model of a two-processor heterogeneous system with time-varying arrival and service rates. We obtain the bounds on the rate of convergence and find the main limiting characteristics…
With the increasing availability of transaction data collected by digital parking meters, paid curbside parking can be advantageously modeled as a network of interdependent queues. In this article we introduce methods for analyzing a…
In this article a special case of an M/G/2-queue is considered, where the two servers are exposed to two types of jobs that are distributed among the servers via a random switch. In this model the asymptotic behaviour of the workload buffer…
We suggest an approach to obtaining general two-sided bounds on the rate of convergence in terms of special "weighted" norms related to total variation. Some important classes of continuous-time Markov chains are considered:…
Heavy-traffic limit theory deals with queues that operate close to criticality and face severe queueing times. Let $W$ denote the steady-state waiting time in the ${\rm GI}/{\rm G}/1$ queue. Kingman (1961) showed that $W$, when…
Queueing networks are notoriously difficult to analyze sans both Markovian and stationarity assumptions. Much of the theoretical contribution towards performance analysis of time-inhomogeneous single class queueing networks has focused on…
Atar and Miyazawa recently introduced a single server queue with queue length dependent arrival and service processes, and name it a multi-level queue. They prove that the heavy traffic limit of its queue length process weakly converges to…
For a GI/GI/1 queue, we show that the average sojourn time under the (blind) Randomized Multilevel Feedback algorithm is no worse than that under the Shortest Remaining Processing Time algorithm times a logarithmic function of the system…
Motivated by a web-server model, we present a queueing network consisting of two layers. The first layer incorporates the arrival of customers at a network of two single-server nodes. We assume that the inter-arrival and the service times…
We consider a discrete time parallel queue, which is two-queue network, where at each time-slot there is a the same batch arrival to both queues and at each queue there is a random service available. The service law at each time-slot for…
Given a random variable $N$ with values in ${\mathbb{N}}$, and $N$ i.i.d. positive random variables $\{\mu_k\}$, we consider a queue with renewal arrivals and $N$ exponential servers, where server $k$ serves at rate $\mu_k$, under two work…
A many-server heavy-traffic FCLT is proved for the $G_t/M/s_t+\mathit {GI}$ queueing model, having time-varying arrival rate and staffing, a general arrival process satisfying a FCLT, exponential service times and customer abandonment…
We consider a load balancing system consisting of $n$ single-server queues working in parallel, with heterogeneous service rates. Jobs arrive to a central dispatcher, which has to dispatch them to one of the queues immediately upon arrival.…
We consider an acyclic network of single-server queues with heterogeneous processing rates. It is assumed that each queue is fed by the superposition of a large number of i.i.d. Gaussian processes with stationary increments and positive…
The presented study elaborates a multi-server priority queueing model considering the pre-emptive repeat policy and phase-type distribution (PH) for retrial process. The incoming heterogeneous calls are categorized as handoff calls and new…
This paper concerns the recurrence structure of the infinite server queue, as viewed through the prism of the maximum dater sequence, namely the time to drain the current work in the system as seen at arrival epochs. Despite the importance…
We consider an $M/G/\infty$ queue with infinite expected service time. We then provide the transience/recurrence classification of the states (the system is said to be at state $n$ if there are $n$ customers being served), observing also…
This self-contained discussion relates the long-run average holding cost per unit time to the long-run average response time per customer in a $G/G/1$ queue with no assumption made on the order of service. The only restriction established…
We study the heavy-traffic limit of the generalized switch operating under MaxWeight, without assuming that the CRP condition is satisfied and allowing for correlated arrivals. The main contribution of this paper is the steady-state mean of…