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A queueing model has $J\ge2$ heterogeneous service stations, each consisting of many independent servers with identical capabilities. Customers of $I\ge2$ classes can be served at these stations at different rates, that depend on both the…
We analyze the so-called Shortest Queue First (SQF) queueing discipline whereby a unique server addresses queues in parallel by serving at any time that queue with the smallest workload. Considering a stationary system composed of two…
Motivated by demand prediction for the custodial prison population in England and Wales, this paper describes an approach to the study of service systems using infinite server queues, where the system has non-empty initial state and the…
In road traffic networks, large traffic volumes may lead to extreme delays. These severe delays are caused by the fact that, whenever the maximum capacity of a road is approached, speeds drop rapidly. Therefore, the focus in this paper is…
Service systems like data centers and ride-hailing are popularly modeled as queueing systems in the literature. Such systems are primarily studied in the steady state due to their analytical tractability. However, almost all applications in…
Retailers use a variety of mechanisms to enable sales and delivery. A relatively new offering by companies is curbside pickup where customers purchase goods online, schedule a pickup time, and come to a pickup facility to receive their…
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…
This paper purpose is to investigate exponential behavior conditions for the infinite servers queue with Poisson arrivals busy period length distribution. It is presented a general theoretical result that is the basis of this work. The…
In this paper we consider a single-server, cyclic polling system with switch-over times. A distinguishing feature of the model is that the rates of the Poisson arrival processes at the various queues depend on the server location. For this…
We consider a heterogeneous queueing system consisting of one large pool of $O(r)$ identical servers, where $r\to\infty$ is the scaling parameter. The arriving customers belong to one of several classes which determines the service times in…
Motivated by the operational problems in click and collect systems, such as curbside pickup programs, we study a joint admission control and capacity allocation problem. We consider a system where arriving customers have preferred service…
We analyze a boarding solution for a transport system in which the number of passengers allowed to enter a transport cabin is automatically controlled. Expressions charac- terizing the stochastic properties of the passenger queue length,…
In this paper one presents method for the computation of convergence bounds for four classes of multiserver queueing systems, described by inhomogeneous Markov chains. Specifically one considers inhomogeneous $M/M/S$ queueing system with…
We consider transmission of packets over queue-length sensitive unreliable links, where packets are randomly corrupted through a noisy channel whose transition probabilities are modulated by the queue-length. The goal is to characterize the…
Metro systems in megacities such as Beijing, Shenzhen and Guangzhou are under great passenger demand pressure. During peak hours, it is common to see oversaturated conditions (i.e., passenger demand exceeds network capacity), which bring…
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…
Let $X$ be the constrained random walk on ${\mathbb Z}_+^2$ with increments $(1,0)$, $(-1,0)$, $(0,1)$ and $(0,-1)$; $X$ represents, at arrivals and service completions, the lengths of two queues working in parallel whose service and…
This paper proposes a novel max-pressure (MP) algorithm that incorporates pedestrian traffic into the MP control architecture. Pedestrians are modeled as being included in one of two groups: those walking on sidewalks and those queued at…
The slow-to-start mechanism is known to play an important role in the particular shape of the Fundamental diagram of traffic and to be associated to hysteresis effects of traffic flow.We study this question in the context of exclusion and…
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…