Stabilization of an overloaded queueing network using measurement-based admission control

Admission control can be employed to avoid congestion in queueing networks subject to overload. In distributed networks the admission decisions are often based on imperfect measurements on the network state. This paper studies how the lack of complete state information affects the system performance by considering a simple network model for distributed admission control. The stability region of the network is characterized and it is shown how feedback signaling makes the system very sensitive to its parameters.Comment: Published at http://dx.doi.org/10.1239/jap/1143936256 in the Journal of Applied Probability (http://projecteuclid.org/jap) by the Applied Probability Trust (http://www.appliedprobability.org/

Lattice path counting and the theory of queues

In this paper we will show how recent advances in the combinatorics of lattice paths can be applied to solve interesting and nontrivial problems in the theory of queues. The problems we discuss range from classical ones like M^a/M^b/1 systems to open tandem systems with and without global blocking and to queueing models that are related to random walks in a quarter plane like the Flatto-Hahn model or systems with preemptive priorities. (author´s abstract)Series: Research Report Series / Department of Statistics and Mathematic

Tandem queueing networks with neighbor blocking and back-offs

We introduce a novel class of tandem queueing networks which arise in modeling the congestion behavior of wireless multi-hop networks with distributed medium access control. These models provide valuable insight in how the network performance in terms of throughput depends on the back-off mechanism that governs the competition among neighboring nodes for access to the medium. The models fall at the interface between classical queueing networks and interacting particle systems, and give rise to high-dimensional stochastic processes that challenge existing methodologies. We present various open problems and conjectures, which are supported by partial results for special cases and limit regimes as well as simulation experiments

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

ASIP tandem queues with consumption

The Asymmetric Inclusion Process (ASIP) tandem queue is a model of stations in series with a gate after each station. At a gate opening, all customers in that station instantaneously move to the next station unidirectionally. In our study, we enhance the ASIP model by introducing the capability for individual customers to independently move from one station to the next, and by allowing both individual customers and batches of customers from any station to exit the system. The model is inspired by the process by which macromolecules are transported within cells. We present a comprehensive analysis of various aspects of the queue length in the ASIP tandem model. Specifically, we provide an exact analysis of queue length moments and correlations and, under certain circumstances, of the queue length distribution. Furthermore, we propose an approximation for the joint queue length distribution. This approximation is derived using three different approaches, one of which employs the concept of the replica mean-field limit. Among other results, our analysis offers insight into the extent to which nutrients can support the survival of a cell.</p

Capacity planning of prisons in the Netherlands

In this paper we describe a decision support system developed to help in assessing the need for various type of prison cells. In particular we predict the probability that a criminal has to be sent home because of a shortage of cells. The problem is modelled through a queueing network with blocking after service. We focus in particular on the new analytical method to solve this network