Exact explicit results are derived for the distribution of the partial busy period of the M/M/c multi-server queue for a general number of servers. A rudimentary spectral method leads to a representation that is amenable to efficient numerical …

We consider multi-component matching systems in heavy traffic consisting of $$K\ge 2$$ K ≥ 2 distinct perishable components which arrive randomly over time at high speed at the assemble-to-order station, and they wait in their respective queues …

We characterize the impact of scheduling policies on the mean response time in nested systems with cancel-on-complete redundancy. We consider not only class- and state-oblivious policies such as FCFS and ROS, but also class-based, and, in …

We present a detailed study of the time-dependent behavior of both the queue-length process and the workload process of various types of preemptive Last-Come-First-Served queueing systems, such as the preemptive repeat different and preemptive …

This paper examines the performance of multi-class, multi-server bipartite queueing systems, where each arriving customer is compatible with only a subset of servers. We focus on the system’s performance under a first-come, first-served-assign …

We consider the optimal scheduling problem in a multiserver queue with impatient customers belonging to multiple classes. We assume that each customer has a random abandonment time, after which the customer leaves the system if its service has not …

Motivated by a service platform, we study a two-sided network where heterogeneous demand (customers) and heterogeneous supply (workers) arrive randomly over time to get matched. Customers and workers arrive with a randomly sampled patience time …

The multi-server queue with non-homogeneous Poisson arrivals and customer abandonment is a fundamental dynamic rate queueing model for large-scale service systems such as call centers and hospitals. Scaling the arrival rates and number of servers …

Service providers routinely share information about upcoming waiting times with their customers, through delay announcements. The need to effectively manage the provision of these announcements has led to a substantial growth in the body of …

An obvious way to simulate a Lévy process X is to sample its increments over time 1 / n, thus constructing an approximating random walk $$X^{(n)}$$ X ( n ) . This paper considers the error of such approximation after the two-sided reflection map …

Extending Ward Whitt’s pioneering work “Fluid Models for Multiserver Queues with Abandonments, Operations Research, 54(1) 37–54, 2006,” this paper establishes a many-server heavy-traffic functional central limit theorem for the overloaded …

In this paper, we develop time-varying fluid models for tandem networks with blocking. Beyond having their own intrinsic value, these mathematical models are also limits of corresponding many-server stochastic systems. We begin by analyzing a …