Related papers: On Erlang Queue with Multiple Arrivals and its Tim…
The paper studies a multiserver retrial queueing system with $m$ servers. Arrival process is a point process with strictly stationary and ergodic increments. A customer arriving to the system occupies one of the free servers. If upon…
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…
Understanding the detailed queueing behavior of a networking session is critical in enabling low-latency services over the Internet. Especially when the packet arrival and service rates at the queue of a link vary over time and moreover…
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…
The infinite-server queueing models with homogeneous and non-homogeneous arrivals of customers and catastrophes are considered. The probability generating functions of joint distributions of numbers of busy servers and served customers, as…
In this work, we consider the case where a source with bursty traffic can adjust the transmission duration in order to increase the reliability. The source is equipped with a queue in order to store the arriving packets. We model the system…
This exposition presents a novel approach to solving an M/M/m queue for the waiting time and the residence time. The motivation comes from an algebraic solution for the residence time of the M/M/1 queue. The key idea is the introduction of…
We study the information-theoretic limit of reliable information processing by a server with queue-length dependent quality of service. We define the capacity for such a system as the number of bits reliably processed per unit time, and…
We consider the problem of staffing large-scale service systems with multiple customer classes and multiple dedicated server pools under joint quality-of-service (QoS) constraints. We first analyze the case in which arrival rates are…
Queueing networks are typically modelled assuming that the arrival process is exogenous, and unaffected by admission control, scheduling policies, etc. In many situations, however, users choose the time of their arrival strategically,…
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 the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal.…
We introduce a novel single-server queue with general retrial times and event-dependent arrivals. This is a versatile model for the study of service systems, in which the server needs a non-negligible time to retrieve waiting customers upon…
Consider an M/M/$s$ queue with the additional feature that the arrival rate is a random variable of which only the mean, variance, and range are known. Using semi-infinite linear programming and duality theory for moment problems, we…
An infinite buffer batch service vacation queue has been studied where service rate of the batch is dependent on the size of the batch and vacation rate is dependent on the queue size at vacation initiation epoch. The arrivals follow the…
Kingman has shown, under very weak conditions on the interarrival- and sevice-time distributions, that First-Come-First-Served minimizes the variance of the waiting time among possible service disciplines. We show, under the same…
In this paper we present results for bivariate exponential distributions which are represented by phase type distributions. The paper extends results from previous publications [5, 14] on this topic by introducing new representations that…
We consider an $M/G/\infty$ queue with infinite expected service time. We then provide the transience/recurrence classification of the states (the system is said to be at state $n$ if there are $n$ customers being served), observing also…
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…
We consider queueing models, where customers arrive according to a continuous-time binomial process on a finite interval. In this arrival process, a total of $K$ customers arrive in the finite time interval $[0,T]$, where arrival times of…