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A queueing model has $J\ge2$ heterogeneous service stations, each consisting of many independent servers with identical capabilities. Customers of $I\ge2$ classes can be served at these stations at different rates, that depend on both the…
When deployed in the real world, machine learning models inevitably encounter changes in the data distribution, and certain -- but not all -- distribution shifts could result in significant performance degradation. In practice, it may make…
We present a new framework for designing nonpreemptive and job-size oblivious scheduling policies in the multiserver-job queueing model. The main requirement is to identify a static and balanced sub-partition of the server set and ensure…
Consider the batch-arrival $GI^X/M/c/N$ model with $c$ servers, general inter-arrival batch times, finite buffer, and exponential service times. Inter-arrival batch times, batch sizes, and service times are $i.i.d.$ and independent of each…
Recently multiserver queues with setup times have been extensively studied because they have applications in power-saving data centers. The most challenging model is the M/M/$c$/Setup queue where a server is turned off when it is idle and…
In this work, we study the stationary distribution of the scaled queue length vector process in multiclass queueing networks operating under static buffer priority service policies. We establish that when subjected to a multi-scale heavy…
We consider a heterogeneous queueing system consisting of one large pool of $O(r)$ identical servers, where $r\to\infty$ is the scaling parameter. The arriving customers belong to one of several classes which determines the service times in…
In this paper we show that in a multiclass Markovian network with unit rate servers, the condition that the average load $\rho$ at every server is less than unity is indeed sufficient for the stability or positive recurrence for \emph{any}…
In this paper one presents method for the computation of convergence bounds for four classes of multiserver queueing systems, described by inhomogeneous Markov chains. Specifically one considers inhomogeneous $M/M/S$ queueing system with…
In network quality of service provisioning, premium services generally require to keep a very small loss probability, which is infeasible to measure directly. The proposed virtual queue scheme estimates the small packet loss probability of…
An exact formula for the equilibrium M/U/1 waiting time density is now effectively known. What began as a numeric exploration became a symbolic banquet. Inverse Laplace transforms provided breadcrumbs in the trail; delay differential…
Traditionally, research focusing on the design of routing and staffing policies for service systems has modeled servers as having fixed (possibly heterogeneous) service rates. However, service systems are generally staffed by people.…
This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix $Q\equiv(q_{ij})_{i,j=1}^d$. Both arrival rates and service rates are depending on…
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…
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…
The presented study elaborates a multi-server priority queueing model considering the pre-emptive repeat policy and phase-type distribution (PH) for retrial process. The incoming heterogeneous calls are categorized as handoff calls and new…
Inventory planning for retail chains requires translating demand forecasts into ordering decisions, including asymmetric shortages and holding costs. The VN2 Inventory Planning Challenge formalizes this setting as a weekly decision-making…
We consider the $M/G/1$ queue with a processor sharing server. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, as well as the unconditional distribution, in various asymptotic limits.…
We study the power spectral density of continuous time Markov chains and explicit its relationship with the eigenstructure of the infinitesimal generator. This result helps us understand the dynamics of the number of customers for a M/M/1…
In many applications, significant correlations between arrivals of load-generating events make the numerical evaluation of the load of a system a challenging problem. Here, we construct very accurate approximations of the workload…