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A key operational challenge for call centers is to decide, in real time, which waiting customer should be served by which available agent. This is known as skill-based routing, and the decision becomes especially difficult in large systems…
The queue system,with Poisson arrivals,constant service time and infinite servers, busy period distribution is intensively studied because, due to its probability density function quite easy interpretation, it may serve as a clue to…
We study randomized experiments in a service system when stochastic congestion can arise from temporarily limited supply or excess demand. Such congestion gives rise to cross-unit interference between the waiting customers, and analytic…
In this paper we study coordinated multipath routing at the flow-level in networks with routes of length one. As a first step the static case is considered, in which the number of flows is fixed. A clustering pattern in the rate allocation…
A many-server queueing system is considered in which customers with independent and identically distributed service times enter service in the order of arrival. The state of the system is represented by a process that describes the total…
We consider a queue to which only a finite pool of $n$ customers can arrive, at times depending on their service requirement. A customer with stochastic service requirement $S$ arrives to the queue after an exponentially distributed time…
We introduce a framework and develop a theory of transitory queueing models. These are models that are not only non-stationary and time-varying but also have other features such as the queueing system operates over finite time, or only a…
Discrete-time queueing system has widespread applications in packet switching networks, internet protocol, Broadband Integrated Services Digital Network (B-ISDN), circuit switched time-division multiple access etc. In this paper, we analyze…
This paper studies multiclass loss systems with two layers of servers, where each server at the first layer is dedicated to a certain customer class, while the servers at the second layer can handle all customer classes. The routing of…
Queueing systems with a single server in which customers wait to be served at a finite number of distinct locations (buffers/queues) are called discrete polling systems. Polling systems in which arrivals of users occur anywhere in a…
We consider a dynamic system with multiple types of customers and servers. Each type of waiting customer or server joins a separate queue, forming a bipartite graph with customer-side queues and server-side queues. The platform can match…
We study a dynamic scheduling problem for a multi-class queueing network with a large pool of statistically identical servers. The arrival processes are Poisson, and service times and patience times are assumed to be exponentially…
We develop a robust queueing network analyzer algorithm to approximate the steady-state performance of a single-class open queueing network of single-server queues with Markovian routing. The algorithm allows non-renewal external arrival…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
Consider a system with $K$ parallel queues in which the server for each queue processes jobs at rate $n$ and the total arrival rate to the system is $nK-\upsilon \sqrt{n}$ where $\upsilon \in (0, \infty)$ and $n$ is large. We study…
A simple analytical solution is proposed for the stationary loss system of two parallel queues with finite capacity $K$, in which new customers join the shortest queue, or one of the two with equal probability if their lengths are equal.…
Proper management of resources whose arrival and consumption are subject to environmental randomness is an intrinsic process in both natural and artificial systems. This phenomenon can be modeled as a queuing process whose arrival…
The model is a "generalized switch", serving multiple traffic flows in discrete time. The switch uses MaxWeight algorithm to make a service decision (scheduling choice) at each time step, which determines the probability distribution of the…
We study a general $k$ dimensional infinite server queues process with Markov switching, Poisson arrivals and where the service times are fat tailed with index $\alpha\in (0,1)$. When the arrival rate is sped up by a factor $n^\gamma$, the…
We consider a service system with an infinite number of exponential servers sharing a finite service capacity. The servers are ordered according to their speed, and arriving customers join the fastest idle server. A capacity allocation is…