Related papers: Heavy Traffic Limit for a Tandem Queue with Identi…
We study a double-ended queue where buyers and sellers arrive to conduct trades. When there is a pair of buyer and seller in the system, they immediately transact a trade and leave. Thus there cannot be non-zero number of buyers and sellers…
We establish a heavy-traffic limit theorem on convergence in distribution for the number of customers in a many-server queue when the number of servers tends to infinity. No critical loading condition is assumed. Generally, the limit…
We consider a multi-server queue in the Halfin-Whitt regime: as the number of servers $n$ grows without a bound, the utilization approaches 1 from below at the rate $\Theta(1/\sqrt{n})$. Assuming that the service time distribution is…
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…
The models studied in the steady state involve two queues which are served either by a single server whose speed depends on the number of jobs present, or by several parallel servers whose number may be controlled dynamically. Job service…
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.…
Demand for studying queueing systems with multiple servers providing correlated services was created about 60 years ago, motivated by various applications. In recent years, the importance of such studies has been significantly increased,…
In this paper we study the maximum queue length $M$ (in terms of the number of customers present) in a busy cycle in the M/G/1 queue. Assume that the service times have a logconvex density. For such (heavy-tailed) service-time distributions…
A special customer must complete service from two servers in series, in either order, each with an M/M/1 queueing system. It is assumed that the two queueing system lengths are independent with initial numbers of customers a and b at the…
We study the $G/\mathit{GI}/\infty$ queue in heavy-traffic using tempered distribution-valued processes which track the age and residual service time of each customer in the system. In both cases, we use the continuous mapping theorem…
Tandem queueing systems are widely-used stochastic models that arise from many real-life service operations systems. Motivated by the desire to understand the trade-off between the performance and complexity of policies for…
In many important real-world queueing settings, arrival and service rates fluctuate over time. We consider the MAMS system, where the arrival and service rates each vary according to an arbitrary finite-state Markov chain, allowing…
We consider multi-component matching systems in heavy traffic consisting of $K\geq 2$ distinct perishable components which arrive randomly over time at high speed at the assemble-to-order station, and they wait in their respective queues…
We consider a sequence of single-server queueing models operating under a service policy that incorporates batches into processor sharing: arriving jobs build up behind a gate while waiting to begin service, while jobs in front of the gate…
This work focuses on time-inhomogeneous Markov chains with two time scales. Our motivations stem from applications in reliability and dependability, queueing networks, financial engineering and manufacturing systems, where two-time-scale…
In this paper we study a two-queue polling model with zero switch-over times and $k$-limited service (serve at most $k_i$ customers during one visit period to queue $i$, $i=1,2$) in each queue. The arrival processes at the two queues are…
This paper studies a single server queue in heavy traffic, with general inter-arrival and service time distributions, where arrival and service rates vary discontinuously as a function of the (diffusively scaled) queue length. It is proved…
We study a many-server queuing system with general service time distribution and state dependent service rates. The dynamics of the system are modeled using measure valued processes which keep track of the residual service times. Under…
A "scheduled" arrival process is one in which the n th arrival is scheduled for time n, but instead occurs at a different time. The difference between the scheduled time and the arrival time is called the perturbation. The sequence of…
In this paper, we investigate the problem of assignment of $K$ identical servers to a set of $N$ parallel queues in a time slotted queueing system. The connectivity of each queue to each server is randomly changing with time; each server…