Related papers: Infinite-server queues with Hawkes input
We study the spatio-temporal prediction problem, which has attracted the attention of many researchers due to its critical real-life applications. In particular, we introduce a novel approach to this problem. Our approach is based on the…
Hawkes Processes are a type of point process which models self-excitement among time events. It has been used in a myriad of applications, ranging from finance and earthquakes to crime rates and social network activity analysis.Recently, a…
A many-server heavy-traffic FCLT is proved for the $G_t/M/s_t+\mathit {GI}$ queueing model, having time-varying arrival rate and staffing, a general arrival process satisfying a FCLT, exponential service times and customer abandonment…
Event-driven systems in fields such as neuroscience, social networks, and finance often exhibit dynamics influenced by continuously evolving external covariates. Motivated by these applications, we introduce a new class of multivariate…
In this paper, we use a machine learning approach to predict the stationary distributions of the number of customers in a single-staiton multi server system. We consider two systems, the first is $c$ homogeneous servers, namely the…
Point processes are widely used statistical models for continuous-time discrete event data, such as medical records, crime reports, and social network interactions, to capture the influence of historical events on future occurrences. In…
We consider a two station cascade system in which waiting or externally arriving customers at station $1$ move to the station $2$ if the queue size of station $1$ including a customer being served is greater than a given threshold level…
We consider a service system model primarily motivated by the problem of efficient assignment of virtual machines to physical host machines in a network cloud, so that the number of occupied hosts is minimized. There are multiple input…
We study a parallel queueing system with multiple types of servers and customers. A bipartite graph describes which pairs of customer-server types are compatible. We consider the service policy that always assigns servers to the first,…
We consider a Markovian clearing queueing system, where the customers are accumulated according to a Poisson arrival process and the server removes all present customers at the completion epochs of exponential service cycles. This system…
We study a many-server queueing model with server vacations, where the population size dynamics of servers and customers are coupled: a server may leave for vacation only when no customers await, and the capacity available to customers is…
We consider an infinite server queue where the arrival and the service rates are both modulated by a stochastic environment governed by an $S$-valued stochastic process $X$ that is ergodic with a limiting measure $\pi\in \mathcal{P}(S)$.…
In this paper we analyze an $M/M/1$ queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a…
We consider a discrete-time parallel service system consisting of $n$ heterogeneous single server queues with infinite capacity. Jobs arrive to the system as an i.i.d. process with rate proportional to $n$, and must be immediately…
We consider a GI/H/n queueing system. In this system, there are multiple servers in the queue. The inter-arrival time is general and independent, and the service time follows hyper-exponential distribution. Instead of stochastic…
In this paper, we analyze a multiserver Markovian queue with customer abandonment i.e. the Erlang-A queue uder a novel framework, i.e. the random impulsive differential equations (RIDEs). This framework captures systems that evolve…
Self-exciting processes of Hawkes type have been used to model various phenomena including earthquakes, neural activities, and views of online videos. Studies of temporal networks have revealed that sequences of social interevent times for…
Modern Internet services, such as those at Google, Yahoo!, and Amazon, handle billions of requests per day on clusters of thousands of computers. Because these services operate under strict performance requirements, a statistical…
Queueing systems with batch Markovian arrival process (BMAP) have paramount applications in the domain of wireless communication. The BMAP has been used to model the superposition of video sources and to approximate the super-position of…
We consider a classical risk process with arrival of claims following a non-stationary Hawkes process. We study the asymptotic regime when the premium rate and the baseline intensity of the claims arrival process are large, and claim size…