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After a short report of results on infinite servers queues systems, focusing on its busy period, using networks of queues with infinite servers nodes a model is constructed to study a two echelons repair system. These repair systems may be…
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 an infinite sequence consisting of agents of several types and goods of several types, with a bipartite compatibility graph between agent and good types. Goods are matched with agents that appear earlier in the sequence using…
We introduce the prioritising exclusion process, a stochastic scheduling mechanism for a priority queueing system in which high priority customers gain advantage by overtaking low priority customers. The model is analogous to a totally…
We consider the FCFS $GI/GI/n$ queue in the Halfin-Whitt heavy traffic regime, and prove bounds for the steady-state probability of delay (s.s.p.d.) for generally distributed processing times. We prove that there exist $\epsilon_1,…
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…
In join the shortest queue networks, incoming jobs are assigned to the shortest queue from among a randomly chosen subset of $D$ queues, in a system of $N$ queues; after completion of service at its queue, a job leaves the network. We also…
We consider general large-scale service systems with multiple customer classes and multiple server (agent) pools, mean service times depend both on the customer class and server pool. It is assumed that the allowed activities (routing…
This paper studies a diffusion model that arises as the limit of a queueing system scheduling problem in the asymptotic heavy traffic regime of Halfin and Whitt. The queueing system consists of several customer classes and many servers…
In this paper, we consider the number of both arrivals and departures seen by a tagged customer while in service in a classical $M/M/1$ processor sharing queue. By exploiting the underlying orthogonal structure of this queuing system…
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…
The non-stationary Erlang-A queue is a fundamental queueing model that is used to describe the dynamic behavior of large scale multi-server service systems that may experience customer abandonments, such as call centers, hospitals, and…
We study the design of dynamic scheduling controls in closed queueing networks with a fixed number of jobs. Each time a server becomes available, the controller has (limited) flexibility in choosing the buffer from which to serve a job. If…
In this paper, we study queueing systems with delayed information that use a generalization of the multinomial logit choice model as its arrival process. Previous literature assumes that the functional form of the multinomial logit model is…
We consider the problem of customer equilibrium behavior of a single server Markovian queue with dynamic control of the service rate. Customers arrive according a Poisson procedure and the system administrator makes a service rate choice…
Nonlinear response occurs naturally when a strong perturbation takes a system far from equilibrium. Despite of its omnipresence in nanoscale systems, it is difficult to predict in a general and efficient way. Here we introduce a way to…
The problem of exact evaluation of the mean service cycle time in tandem systems of single-server queues with both infinite and finite buffers is considered. It is assumed that the interarrival and service times of customers form sequences…
This paper studies an infinite buffer single server queueing model with exponentially distributed service times and negative arrivals. The ordinary (positive) customers arrive in batches of random size according to renewal arrival process,…
The performance of non-preemptive M/M/1 queueing system with two priority is analyzed. By using complementary variable method to make vector Markov process and analyzing the state-change equations of the queueing system, the generating…
We investigate the long-run behavior of single-server queues with Hawkes arrivals and general service distributions and related optimization problems. In detail, utilizing novel coupling techniques, we establish finite moment bounds for the…