Related papers: An infinite server system with packing constraints…
We consider the following distributed service model: jobs with unit mean, general distribution, and independent processing times arrive as a renewal process of rate $\lambda n$, with $0<\lambda<1$, and are immediately dispatched to one of…
Many networking-related settings can be modeled by Markov-modulated infinite-server systems. In such models, the customers' arrival rates and service rates are modulated by a Markovian background process, additionally, there are infinitely…
We consider the allocation of limited resources to heterogeneous customers who arrive in an online fashion. We would like to allocate the resources "fairly", so that no group of customers is marginalized in terms of their overall service…
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…
A multiclass queueing system is considered, with heterogeneous service stations, each consisting of many servers with identical capabilities. An optimal control problem is formulated, where the control corresponds to scheduling and routing,…
We study a system, where a random flow of customers is served by servers (called agents) invited on-demand. Each invited agent arrives into the system after a random time; after each service completion, an agent returns to the system or…
Two independent Poisson streams of jobs flow into a single-server service system having a limited common buffer that can hold at most one job. If a type-i job (i=1,2) finds the server busy, it is blocked and routed to a separate type-i…
We consider a processor sharing storage allocation model, which has m primary holding spaces and infinitely many secondary ones, and a single processor servicing the stored items (customers). All of the spaces are numbered and ordered. An…
In this paper, we investigate the problem of assignment of $K$ identical servers to a set of $N$ parallel queues in a time slotted queueing system. The connectivity of each queue to each server is randomly changing with time; each server…
We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by shot noise. A shot-noise rate emerges as a natural model, if the arrival rate tends…
Consider a queueing system consisting of multiple servers. Jobs arrive over time and enter a queue for service; the goal is to minimize the size of this queue. At each opportunity for service, at most one server can be chosen, and at most…
A broad class of parallel server systems is considered, for which we prove the steady-state asymptotic independence of server workloads, as the number of servers goes to infinity, while the system load remains sub-critical. Arriving jobs…
We analyze an M/M/1 queue with a service discipline in which customers, upon arriving when the server is busy, search a sequence of stations for a vacant station at which to wait, and in which the server, upon becoming free when one or more…
This work considers a many-server queueing system in which customers with i.i.d., generally distributed service times enter service in the order of arrival. The dynamics of the system is represented in terms of a process that describes the…
Motivated by the Quality-of-Service (QoS) buffer management problem, we consider online scheduling of packets with hard deadlines in a finite capacity queue. At any time, a queue can store at most $b \in \mathbb Z^+$ packets. Packets arrive…
In order for an e-commerce platform to maximize its revenue, it must recommend customers items they are most likely to purchase. However, the company often has business constraints on these items, such as the number of each item in stock.…
In this paper we study the number of customers in infinite-server queues with a self-exciting (Hawkes) arrival process. Initially we assume that service requirements are exponentially distributed and that the Hawkes arrival process is of a…
To perform a queuing analysis or design in a communications context, we need to estimate the values of the input parameters, specifically the mean of the arrival rate and service time. In this paper, we propose an approach for estimating…
We introduce a general model of resource allocation with customer choice. In this model, there are multiple resources that are available over a finite horizon. The resources are non-replenishable and perishable. Each unit of a resource can…
In this paper we look at content placement in the high-dimensional regime: there are n servers, and O(n) distinct types of content. Each server can store and serve O(1) types at any given time. Demands for these content types arrive, and…