Loss systems in a random environment

We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service process is completely blocked: Service is interrupted and newly arriving customers are lost. We prove an if-and-only-if-condition for a product form steady state distribution of the joint queueing-environment process. A consequence is a strong insensitivity property for such systems. We discuss several applications, e.g. from inventory theory and reliability theory, and show that our result extends and generalizes several theorems found in the literature, e.g. of queueing-inventory processes. We investigate further classical loss systems, where due to finite waiting room loss of customers occurs. In connection with loss of customers due to blocking by the environment and service interruptions new phenomena arise. We further investigate the embedded Markov chains at departure epochs and show that the behaviour of the embedded Markov chain is often considerably different from that of the continuous time Markov process. This is different from the behaviour of the standard M/G/1, where the steady state of the embedded Markov chain and the continuous time process coincide. For exponential queueing systems we show that there is a product form equilibrium of the embedded Markov chain under rather general conditions. For systems with non-exponential service times more restrictive constraints are needed, which we prove by a counter example where the environment represents an inventory attached to an M/D/1 queue. Such integrated queueing-inventory systems are dealt with in the literature previously, and are revisited here in detail

Queueing Systems with Service Interruptions: An Approximation Model

International audienc

Analysis of the finite-source multiclass priority queue with an unreliable server and setup time

In this article, we study a queueing system serving multiple classes of customers. Each class has a finite-calling population. The customers are served according to the preemptive-resume priority policy. We assume general distributions for the service times. For each priority class, we derive the steady-state system size distributions at departure/arrival and arbitrary time epochs. We introduce the residual augmented process completion times conditioned on the number of customers in the system to obtain the system time distribution. We then extend the model by assuming that the server is subject to operation-independent failures upon which a repair process with random duration starts immediately. We also demonstrate how setup times, which may be required before resuming interrupted service or picking up a new customer, can be incorporated in the model

Simple bounds for queueing systems with breakdowns

Computationally attractive and intuitively obvious simple bounds are proposed for finite service systems which are subject to random breakdowns. The services are assumed to be exponential. The up and down periods are allowed to be generally distributed. The bounds are based on product-form modifications and depend only on means. A formal proof is presented. This proof is of interest in itself. Numerical support indicates a potential usefulness for quick engineering and performance evaluation purposes

Distributional little's law for queues with heterogeneous server interruptions

Distributional forms of Little's law relate the steady-state distributions of the number of customers in a queueing system (system content) and the time a customer spends in the system (delay). A new law for discrete-time multiserver queues is discussed, with single-slot service times, a first-come-first-served discipline and heterogeneous server interruptions

Healthcare queueing models.

Healthcare systems differ intrinsically from manufacturing systems. As such, they require a distinct modeling approach. In this article, we show how to construct a queueing model of a general class of healthcare systems. We develop new expressions to assess the impact of service outages and use the resulting model to approximate patient flow times and to evaluate a number of practical applications. We illustrate the devastating impact of service interruptions on patient flow times and show the potential gains obtained by pooling hospital resources. In addition, we present an optimization model to determine the optimal number of patients to be treated during a service session.Operations research; Health care evaluation mechanisms; Organizational efficiency; Management decision support systems; Time management; Queueing theory;

Modeling a healthcare system as a queueing network:The case of a Belgian hospital.

The performance of health care systems in terms of patient flow times and utilization of critical resources can be assessed through queueing and simulation models. We model the orthopaedic department of the Middelheim hospital (Antwerpen, Belgium) focusing on the impact of outages (preemptive and nonpreemptive outages) on the effective utilization of resources and on the flowtime of patients. Several queueing network solution procedures are developed such as the decomposition and Brownian motion approaches. Simulation is used as a validation tool. We present new approaches to model outages. The model offers a valuable tool to study the trade-off between the capacity structure, sources of variability and patient flow times.Belgium; Brownian motion; Capacity management; Decomposition; Health care; Healthcare; Impact; Model; Models; Performance; Performance measurement; Queueing; Queueing theory; Simulation; Stochastic processes; Structure; Studies; Systems; Time; Tool; Validation; Variability;