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The Poisson distribution is the probability distribution of the number of independent events in a given period of time. Although the Poisson distribution appears ubiquitously in various stochastic dynamics of gene expression, both as…
A non-homogeneous Poisson cluster model is studied, motivated by insurance applications. The Poisson center process which expresses arrival times of claims, triggers off cluster member processes which correspond to number or amount of…
Motivated by the growing interest in today's massive parallel computing capabilities we analyze a queueing network with many servers in parallel to which jobs arrive a according to a Poisson process. Each job, upon arrival, is split into…
We study a single-server priority queue with a finite number of classes, in which the arrivals follow a fractional Poisson process of index $\alpha \in (0,1]$ and the service completions are triggered by an independent fractional Poisson…
In small cell networks, high mobility of users results in frequent handoff and thus severely restricts the data rate for mobile users. To alleviate this problem, we propose to use heterogeneous, two-tier network structure where static users…
The arrival process of bidders and bids in online auctions is important for studying and modeling supply and demand in the online marketplace. A popular assumption in the online auction literature is that a Poisson bidder arrival process is…
In a circuit-switched network, traffic can be characterized by several factors that define how communication resources are allocated and utilized during a connection. The amount of traffic basically determines how frequently connection…
We consider energy minimization for data-intensive applications run on large number of servers, for given performance guarantees. We consider a system, where each incoming application is sent to a set of servers, and is considered to be…
A discrete-time random process is described which can generate bursty sequences of events. A Bernoulli process, where the probability of an event occurring at time $t$ is given by a fixed probability $x$, is modified to include a memory…
Arrival processes to service systems often display fluctuations that are larger than anticipated under the Poisson assumption, a phenomenon that is referred to as overdispersion. Motivated by this, we analyze a class of discrete stochastic…
Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects we devise an analytically solvable model…
Edge-caching is recognized as an efficient technique for future cellular networks to improve network capacity and user-perceived quality of experience. To enhance the performance of caching systems, designing an accurate content request…
We consider the job assignment problem in a multi-server system consisting of $N$ parallel processor sharing servers, categorized into $M$ ($\ll N$) different types according to their processing capacity or speed. Jobs of random sizes…
Operations Research approaches to surgical scheduling are becoming increasingly popular in both theory and practice. Often these models neglect stochasticity in order to reduce the computational complexity of the problem. We wish to provide…
Redundant storage maintains the performance of distributed systems under various forms of uncertainty. This paper considers the uncertainty in node access and download service. We consider two access models under two download service…
We describe mechanisms for the allocation of a scarce resource among multiple users in a way that is efficient, fair, and strategy-proof, but when users do not know their resource requirements. The mechanism is repeated for multiple rounds…
The location of active users is an important factor in the performance analysis of mobile multicell networks, but it is difficult to quantify due to the wide variety of user mobility and session patterns. In particular, the channel holding…
We consider the single server queue with service in random order. For a large class of heavy-tailed service time distributions, we determine the asymptotic behavior of the waiting time distribution. For the special case of Poisson arrivals…
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 a service system with two Poisson arrival queues. A server chooses which queue to serve at each moment. Once a queue is served, all the customers will be served within a fixed amount of time. This model is useful in studying…