A heavy traffic limit theorem for a class of open queueing networks with finite buffers
Queueing Systems: Theory and Applications
Designing a Call Center with Impatient Customers
Manufacturing & Service Operations Management
Patient Choice in Kidney Allocation: The Role of the Queueing Discipline
Manufacturing & Service Operations Management
A Diffusion Approximation for a GI/GI/1 Queue with Balking or Reneging
Queueing Systems: Theory and Applications
Call Centers with Impatient Customers: Many-Server Asymptotics of the M/M/n + G Queue
Queueing Systems: Theory and Applications
Fluid Models for Multiserver Queues with Abandonments
Operations Research
Mathematics of Operations Research
The Impact of Delay Announcements in Many-Server Queues with Abandonment
Operations Research
Nurse Staffing in Medical Units: A Queueing Perspective
Operations Research
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In this paper we consider a single-server queue fed by K independent renewal arrival streams, each representing a different job class. Jobs are processed in a FIFO fashion, regardless of class. The total amount of work arriving to the system exceeds the server's capacity. That is, the nominal traffic intensity of the system is assumed to be greater than one. Jobs arriving to the system grow impatient and abandon the queue after a random amount of time if service has not yet begun. Interarrival, service, and abandonment times are assumed to be generally distributed and class specific. We approximate this system using both fluid and diffusion limits. To this end, we consider a sequence of systems indexed by n in which the arrival and service rates are proportional to n; the abandonment distribution remains fixed across the sequence. In our first main result, we show that in the limit as n tends to infinity, the virtual waiting time process converges to a limiting deterministic process. This limit may be characterized as the solution to a first-order ordinary differential equation ODE. Specific examples are then presented for which the ODE may be explicitly solved. In our second main result, we refine the deterministic fluid approximation by showing that the fluid-centered and diffusion-scaled virtual waiting time process weakly converges to an Ornstein-Uhlenbeck process whose drift and infinitesimal variance both vary over time. This process may also be solved for explicitly, thus yielding approximations to the transient as well as steady-state behavior of the virtual waiting time process.