Applied Probability and Queues (Stochastic Modelling and Applied Probability)

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Large tail probabilities are important as they reflect the risk of large losses, however, analytic or numerical expressions are not available. We propose several simulation algorithms which are based on an asymptotic analysis of the distribution of the counting variable and on the reproducibility property of the claim distribution.

We conclude by numerical experiments of these algorithms. Upon arrival, each customer receives from the system manager some information about his or her expected quality of service for example, the expected waiting time in the queue, based on the current queue size which is unobservable by the arriving customer , and may then decide whether to balk or join the system. The customers' preferences, which may be heterogeneous, are captured by a demand curve.

The manager is committed to truth telling, but can provide partial information. We ask what information should be provided to arriving customers to maximize the throughput, namely the fraction of customers that choose to join. This question is formulated within the general framework of Bayesian persuasion games.

Concrete solutions are derived, whose form depends on the convexity or concavity properties of the demand curve. FCFS Parallel Service Systems and Matching Models We consider three parallel service models in which customers of several types are served by several types of servers subject to a bipartite compatibility graph, and the service policy is first come first served.

Two of the models have a fixed set of servers. The first is a queueing model in which arriving customers are assigned to the longest idling compatible server if available, or else queue up in a single queue, and servers that become available pick the longest waiting compatible customer, as studied by Adan and Weiss, The second is a redundancy service model where arriving customers split into copies that queue up at all the compatible servers, and are served in each queue on FCFS basis, and leave the system when the first copy completes service, as studied by Gardner et al.

The third model is a matching queueing model with a random stream of arriving servers. Arriving customers queue in a single queue and arriving servers match with the first compatible customer and leave the system at the moment of arrival, or they leave without a customer. The last model is relevant to organ transplants, to housing assignments, to adoptions and many other situations. We study the relations between these models, and show that they are closely related to the FCFS infinite bipartite matching model, in which two infinite sequences of customers and servers of several types are matched FCFS according to a bipartite compatibility graph, as studied by Busic et al.

Dynamic Allocation of Stochastically-Arriving Flexible Resources to Random Streams of Objects with Application to Kidney Cross-Transplantation Two distinct random streams of discrete objects flow into a system and queue in two separate lines. In parallel, two distinct types of resources arrive stochastically over time.

Applied Probability and Queues

Upon arrival, each resource unit is matched with a waiting object. One resource type is 'flexible' and can be allocated to either one of the object types. However, units of the other, non-flexible, resource type can be allocated only to units of one specific object type. The allocation probabilities are not fixed and may depend on both queue sizes of the two objects. If a resource unit is not allocated immediately, it is lost.

The goal is to find an optimal state-dependent probabilistic dynamic allocation policy. We formulate the system as a two-dimensional Markov process, analyze its probabilistic behavior, and derive its performance measures.

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We then apply the model to the problem of organ cross-transplantation and propose a novel measure of system effectiveness, called Expected Value of Transplantation EVT , based on the histocompatibility between organs and candidates. In contrast with the light-tailed case, proving a LDP requires the development of a different framework. Other attendees will have to make their own arrangements. This trip will take about one and a half hour.

Many low cost carriers also fly to Eindhoven Airport. There is a bus connection to the Eindhoven central railway station from the airport. The University can be reached easily by car from the highways leading to Eindhoven. The meeting-room is equipped with a data projector, an overhead projector, a projection screen and a blackboard.

The workshop officer will be present for the duration of the conference, taking care of the administrative aspects and the day-to-day running of the conference: registration, issuing certificates and receipts, etc. View All Events. Oct 2, - Oct 4, Stella Kapodistria Performance analysis for random time-limited polling models We consider a polling model with a service discipline based on the randomly timed gated service: the server resides at a queue for a random amount time and does not switch even if the queue becomes empty but only when the random residing clock expires.

Markov Decision Processes in Practice. Invited talks, refereed proceedings and other conference outputs.

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Applied Probability and Queues Stochastic Modelling and Applied Probability

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Bean, N. Motivated by models for customer contact centres, Dr Buke presented work on multi-server queueing models in which the service rates are independent observations from a given distribution. The work focuses on large-scale limiting behaviour and the corresponding fairness of the system. A biological model for protein synthesis by RNA motivates this study of a queueing system whose input is a Cox process that is, a Poisson process with random rate.