OR/MS research in disaster operations management

Poission process and related processes renewal-reward processes discrete-time Markov chains continuous-time Markov chains Markov chains and queues discrete-time Markov decision processes semi-Markov decision processes advanced renewal theory algorithms analysis of queuing models useful tools in applied probability useful probability distributions generating functions the discrete fast Fourier transform Laplace transformtheory numerical Laplace inversion the root-finding problem.

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A First Course in Stochastic Models

Applied Probability and Queues.

/pdf/reversibility-and-stochastic-networks-17kl9p5ino.pdf

Reversibility and Stochastic Networks

Optimization modeling has become a powerful tool to tackle emergency logistics problems since its first adoption in maritime disaster situations in the 1970s. Using techniques of content analysis, this paper reviews optimization models utilized in emergency logistics. Disaster operations can be performed before or after disaster occurrence. Short-notice evacuation, facility location, and stock pre-positioning are drafted as the main pre-disaster operations, while relief distribution and casualty transportation are categorized as post-disaster operations. According to these operations, works in the literature are broken down into three parts: facility location, relief distribution and casualty transportation, and other operations. For the first two parts, the literature is structured and analyzed based on the model types, decisions, objectives, and constraints. Finally, through the content analysis framework, several research gaps are identified and future research directions are proposed.

Optimization models in emergency logistics: A literature review

Analysis of an M/G/1 queue with constant repeated attempts and server vacations

We consider anM2/G2/1 type queueing system which serves two types of calls. In the case of blocking the first type customers can be queued whereas the second type customers must leave the service area but return after some random period of time to try their luck again. This model is a natural generalization of the classicM2/G2/1 priority queue with the head-of-theline priority discipline and the classicM/G/1 retrial queue. We carry out an extensive analysis of the system, including existence of the stationary regime, embedded Markov chain, stochastic decomposition, limit theorems under high and low rates of retrials and heavy traffic analysis.

On the single server retrial queue with priority customers

We are concerned with the main multiserver retrial queue of M/M/c type with exponential repeated attempts. It is known that an analytical solution of this queueing model is difficult and does not lead to numerical implementation. Based on appropriate understanding of the physical behavior, an efficient and numerically stable algorithm for computing the stationary distribution of the system state is developed. Numerical calculations are done to compare our approach with the existing approximations.

Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue

Analysis of multiserver queues with constant retrial rate

This paper deals with a service system in which the processor must serve two types of impatient units. In the case of blocking, the first type units leave the system whereas the second type units enter a pool and wait to be processed later. We develop an exhaustive analysis of the system including embedded Markov chain, fundamental period and various classical stationary probability distributions. More specific performance measures, such as the number of lost customers and other quantities, are also considered. The mathematical analysis of the model is based on the theory of Markov renewal processes, in Markov chains of M/G/1 type and in expressions of 'Takacs' equation' type. QUEUES WITH IMPATIENT UNITS AND REPEATED ATTEMPTS; TAKACS' EQUATION;

Jesús R. Artalejo

Papers

Analysis of an M/G/1 queue with constant repeated attempts and server vacations

On the single server retrial queue with priority customers

Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue

Analysis of multiserver queues with constant retrial rate

Analysis of an M/G/1 Queue with Two Types of Impatient Units