458 research outputs found
Performance analysis of time-dependent queueing systems: survey and classification
Many queueing systems are subject to time-dependent changes in system parameters, such as the arrival
rate or number of servers. Examples include time-dependent call volumes and agents at inbound call
centers, time-varying air traffic at airports, time-dependent truck arrival rates at seaports, and cyclic message volumes in computer systems.There are several approaches for the performance analysis of queueing systems with deterministic parameter changes over time. In this survey, we develop a classification scheme that groups these approaches according to their underlying key ideas into (i) numerical and analytical solutions,(ii)approaches based on models with piecewise constant parameters, and (iii) approaches based on mod-ified system characteristics. Additionally, we identify links between the different approaches and provide a survey of applications that are categorized into service, road and air traffic, and IT systems
How to Staff when Customers Arrive in Batches
In settings as diverse as autonomous vehicles, cloud computing, and pandemic
quarantines, requests for service can arrive in near or true simultaneity with
one another. This creates batches of arrivals to the underlying queueing
system. In this paper, we study the staffing problem for the batch arrival
queue. We show that batches place a significant stress on services, and thus
require a high amount of resources and preparation. In fact, we find that there
is no economy of scale as the number of customers in each batch increases,
creating a stark contrast with the square root safety staffing rules enjoyed by
systems with solitary arrivals of customers. Furthermore, when customers arrive
both quickly and in batches, an economy of scale can exist, but it is weaker
than what is typically expected. Methodologically, these staffing results
follow from novel large batch and hybrid large-batch-and-large-rate limits of
the general multi-server queueing model. In the pure large batch limit, we
establish the first formal connection between multi-server queues and storage
processes, another family of stochastic processes. By consequence, we show that
the limit of the batch scaled queue length process is not asymptotically
normal, and that, in fact, the fluid and diffusion-type limits coincide. This
is what drives our staffing analysis of the batch arrival queue, and what
implies that the (safety) staffing of this system must be directly proportional
to the batch size just to achieve a non-degenerate probability of customers
waiting
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