arXiv subjects

Britt W. J. Mathijsen

Publications and source records attributed to Britt W. J. Mathijsen.

5 recordsLinked to original sources

arXiv2019

Economies-of-scale in resource sharing systems: tutorial and partial review of the QED heavy-traffic regime

Multi-server queueing systems describe situations in which users require service from multiple parallel servers. Examples include check-in lines at airports, waiting rooms in hospitals, queues in contact centers, data buffers in wireless networks, and delayed service in cloud data centers. These are all situations with jobs (clients, patients, tasks) and servers (agents, beds, processors) that have large capacity levels, ranging from the order of tens (checkouts) to thousands (processors). This survey investigates how to design such systems to exploit resource pooling and economies-of-scale. In particular, we review the mathematics behind the Quality-and-Efficiency Driven (QED) regime, which lets the system operate close to full utilization, while the number of servers grows simultaneously large and delays remain manageable. Aimed at a broad audience, we describe in detail the mathematical concepts for the basic Markovian many-server system, and only provide sketches or references for more advanced settings related to e.g. load balancing, overdispersion, parameter uncertainty, general service requirements and queueing networks. While serving as a partial survey of a massive body of work, the tutorial is not aimed to be exhaustive.

math.PR↗

arXiv2017

Asymptotic dimensioning of stochastic service systems

Stochastic service systems describe situations in which customers compete for service from scarce resources. Think of check-in lines at airports, waiting rooms in hospitals or queues in supermarkets, where the scarce resource is human manpower. Next to these traditional settings, resource sharing is also important in large-scale service systems such as the internet, wireless networks and cloud computing facilities. In these virtual environments, geographical conditions do not restrict the system size, paving the way for the emergence of large-scale resource sharing networks. This thesis investigates how to design large-scale systems in order to achieve the dual goal of operational efficiency and quality-of-service, by which we mean that the system is highly occupied and hence efficiently utilizes the expensive resources, while at the same time, the level of service, experienced by customers, remains high.

math.PR↗

arXiv2017

Robust heavy-traffic approximations for service systems facing overdispersed demand

Arrival processes to service systems often display fluctuations that are larger than anticipated under the Poisson assumption, a phenomenon that is referred to as overdispersion. Motivated by this, we analyze a class of discrete stochastic models for which we derive heavy-traffic approximations that are scalable in the system size. Subsequently, we show how this leads to novel capacity sizing rules that acknowledge the presence of overdispersion. This, in turn, leads to robust approximations for performance characteristics of systems that are of moderate size and/or may not operate in heavy traffic.

math.PR↗

arXiv2016

The restricted Erlang-R Queue: Finite-size effects in service systems with returning customers

Motivated by health care systems with repeated services that have both personnel (nurse and physician) and space (beds) constraints, we study a restricted version of the Erlang-R model. The space restriction policies we consider are blocking or holding in a pre-entrant queue. We develop many-server approximations for the system performance measures when either policy applies, and explore the connection between them. We show that capacity allocation of both resources should be determined simultaneously, and derive the methodology to determine it explicitly. We show that the system dynamics is captured by the fraction of needy time in the network, and that returning customers should be accounted for both in steady-state and time-varying conditions. We demonstrate the application of our policies in two case studies of resource allocation in hospitals.

math.PR↗

arXiv2014

Novel heavy-traffic regimes for large-scale service systems

We introduce a family of heavy-traffic regimes for large scale service systems, presenting a range of scalings that include both moderate and extreme heavy traffic, as compared to classical heavy traffic. The heavy-traffic regimes can be translated into capacity sizing rules that lead to Economies-of-Scales, so that the system utilization approaches 100% while congestion remains limited. We obtain heavy-traffic approximations for stationary performance measures in terms of asymptotic expansions, using a non-standard saddle point method, tailored to the specific form of integral expressions for the performance measures, in combination with the heavy-traffic regimes.

math.PR↗