Related papers: Heavy-traffic limits for waiting times in many-ser…
In order to obtain Markov heavy-traffic approximations for infinite-server queues with general non-exponential service-time distributions and general arrival processes, possibly with time-varying arrival rates, we establish heavy-traffic…
We consider a load balancing system comprised of a fixed number of single server queues, operating under the well-known Join-the-Shortest Queue policy, and where jobs/customers are impatient and abandon if they do not receive service after…
We consider a two-node tandem queueing network in which the upstream queue is M/G/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. We investigate…
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…
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 study many-server queues with abandonment in which customers have general service and patience time distributions. The dynamics of the system are modeled using measure- valued processes, to keep track of the residual service and patience…
This paper addresses the analysis of the queue-length process of single-server queues under overdispersion, i.e., queues fed by an arrival process for which the variance of the number of arrivals in a given time window exceeds the…
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…
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…
This paper presents a heavy-traffic analysis of the behavior of a single-server queue under an Earliest-Deadline-First (EDF) scheduling policy in which customers have deadlines and are served only until their deadlines elapse. The…
In this thesis, we study the queueing systems with heterogeneous servers and service rate uncertainty under the Halfin-Whitt heavy traffic regime. First, we analyse many server queues with abandonments when service rates are i.i.d. random…
This work considers a many-server queueing system in which impatient customers with i.i.d., generally distributed service times and i.i.d., generally distributed patience times enter service in the order of arrival and abandon the queue if…
Inspired by the work of Atar and Miyazawa [1] (2026) as well as applications to energy-saving problems, we are interested in the heavy-traffic limit of the stationary queue length distribution, which is not addressed in [1]. In this paper,…
A many-server queueing system is considered in which customers arrive according to a renewal process and have service and patience times that are drawn from two independent sequences of independent, identically distributed random variables.…
We study a double-ended queue which consists of two classes of customers. Whenever there is a pair of customers from both classes, they are matched and leave the system immediately. The matching follows first-come-first-serve principle. If…
This paper presents a second-order heavy traffic analysis of a single server queue that processes customers having deadlines using the earliest-deadline-first scheduling policy. For such systems, referred to as real-time queueing systems,…
We consider an overloaded multiclass nonidling first-in-first-out single-server queue with abandonment. The interarrival times, service times, and deadline times are sequences of independent and identically, but generally distributed random…
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…
We consider a two-node tandem queueing network in which the upstream queue is GI/GI/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. To…
We consider many-server queueing systems with heterogeneous exponential servers and renewal arrivals. The service rate of each server is a random variable drawn from a given distribution. We develop a framework for analyzing the heavy…