Related papers: Construction of a stationary queue with impatient …
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
We consider a stochastic, dynamic job scheduling problem, formulated as a queueing control problem, in which a single server processes jobs of different types that arrive according to independent Poisson processes. The problem is defined on…
We introduce a multiclass single-server queueing system in which the arrival rates depend on the current job in service. The system is characterized by a matrix of arrival rates in lieu of a vector of arrival rates. Our proposed model…
We model a long queue of humans by a continuous-space model in which, when a customer moves forward, they stop a random distance behind the previous customer, but do not move at all if their distance behind the previous customer is below a…
This paper analyzes a service system modeled as a single-server queue, in which the service provider aims to dynamically maximize the expected revenue per unit of time. This is achieved by constructing a stochastic gradient descent…
We consider a system with N unit-service-rate queues in tandem, with exogenous arrivals of rate lambda at queue 1, under a back-pressure (MaxWeight) algorithm: service at queue n is blocked unless its queue length is greater than that of…
In recent years a number of models involving different compatibilities between jobs and servers in queueing systems, or between agents and resources in matching systems, have been studied, and, under Markov assumptions and appropriate…
In this paper we present a stability criterion for finite measure-valued stochastic recursions, generalizing Loynes's Theorem to spaces of measures. This result provides conditions for the reach of a "total stationary state" for the queue…
This paper studies statistical inference in a network of infinite-server queues, with the aim of estimating the underlying parameters (routing matrix, arrival rates, parameters pertaining to the service times) using observations of the…
A service system with multiple types of customers, arriving according to Poisson processes, is considered. The system is heterogeneous in that the servers also can be of multiple types. Each customer has an independent exponentially…
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.…
We investigate the transient and stationary queue-length distributions of a class of service systems with correlated service times. The classical $M^X/G/1$ queue with semi-Markov service times is the most prominent example in this class and…
We investigate Markovian queues that are examined by a controller at random times determined by a Poisson process. Upon examination, the controller sets the service speed to be equal to the minimum of the current number of customers in the…
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…
In continuous time, customers arrive at random. Each waits until one of $c$ servers is available; each thereafter departs at random. The distribution of maximum line length of idle customers was studied over 25 years ago. We revisit two…
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.…
Burke's theorem can be seen as a fixed-point result for an exponential single-server queue; when the arrival process is Poisson, the departure process has the same distribution as the arrival process. We consider extensions of this result…
We give a recursive construction of the stationary distribution of multi-type asymmetric simple exclusion processes on a finite ring or on the infinite line $Z$. The construction can be interpreted in terms of "multi-line diagrams" or…
We study a vacation-type queueing model, and a single-server multi-queue polling model, with the special feature of retrials. Just before the server arrives at a station there is some deterministic glue period. Customers (both new arrivals…
We consider a Markovian single server queue with impatient customers. There is a customer abandonment cost and a holding cost for customers in the system. We consider two versions of the problem. In the first version, customers pay a reward…