M. J. Lopez-Herrero

Analysis of a Multiserver Queue with Setup Times

This paper deals with the analysis of an M/M/c queueing system with setup times. This queueing model captures the major characteristics of phenomena occurring in production when the system consists in a set of machines monitored by a single operator. We carry out an extensive analysis of the system including limiting distribution of the system state, waiting time analysis, busy period and maximum queue length.

Cellular mobile networks with repeated calls operating in random environment

Many of the currently used cellular networks have been constructed on the premise that the retrial phenomenon is negligible and the operating environment is static. However, a proper modeling of the mobile cellular network cannot ignore the existence of repeated calls. Moreover, real systems often operate in varying environment conditions. In this paper, we show how the matrix-analytic formalism gives one the ability to construct and study versatile cellular mobile networks with user retrials operating in random environment. More concretely, we investigate two four-dimensional Markovian models which allow us to represent two different options for the use of the guard channel concept. We put emphasis on the numerical evaluation of the redial behavior and the environmental factors on the system performance. This implies the performance analysis of a variety of descriptors including blocking probabilities (handover and fresh calls), mean average analysis, and waiting time in orbit.

NUMERICAL ANALYSIS OF(S, S) INVENTORY SYSTEMS WITH REPEATED ATTEMPTS

This paper deals with a continuous review (s,S) inventory system where arriving demands finding the system out of stock, leave the service area and repeat their request after some random time. This assumption introduces a natural alternative to classical approaches based either on lost demand models or on backlogged models. The stochastic model formulation is based on a bidimensional Markov process which is numerically solved to investigate the essential operating characteristics of the system. An optimal design problem is also considered.

On the number of recovered individuals in the SIS and SIR stochastic epidemic models.

The basic models of infectious disease dynamics (the SIS and SIR models) are considered. Particular attention is paid to the number of infected individuals that recovered and its relationship with the final epidemic size. We investigate this descriptor both until the extinction of the epidemic and in transient regime. Simple and efficient methods to obtain the distribution of the number of recovered individuals and its moments are proposed and discussed with respect to the previous work. The methodology could also be extended to other stochastic epidemic models. The theory is illustrated by numerical experiments, which demonstrate that the proposed computational methods can be applied efficiently. In particular, we use the distribution of the number of individuals removed in the SIR model in conjunction with data of outbreaks of ESBL observed in the intensive care unit of a Spanish hospital.

On the busy period of the M/G/1 retrial queue

The M/G/1 queue with repeated attempts is considered. A customer who finds the server busy, leaves the service area and joins a pool of unsatisfied customers. Each customer in the pool repeats his demand after a random amount of time until he finds the server free. We focus on the busy period L of the M/G/1

Algorithmic approximations for the busy period distribution of the M/M/c retrial queue

retrial queue. The structure of the busy period and its analysis in terms of Laplace transforms have been discussed by several authors. However, this solution has serious limitations in practice. For instance, we cannot compute the first moments of L by direct differentiation. This paper complements the existing work and provides a direct method of calculation for the second moment of L.

The maximum number of infected individuals in SIS epidemic models: Computational techniques and quasi-stationary distributions

Abstract In this paper we deal with the main multiserver retrial queue of M / M / c type with exponential repeated attempts. This model is known to be analytically intractable due to the spatial heterogeneity of the underlying Markov chain, caused by the retrial feature. For this reason several models have been proposed for approximating its stationary distribution, that lead to satisfactory numerical implementations. This paper extends these studies by developing efficient algorithmic procedures for calculating the busy period distribution of the main approximation models of Wilkinson [Wilkinson, R.I., 1956. Theories for toll traffic engineering in the USA, The Bell System Technical Journal 35, 421–514], Falin [Falin, G.I., 1983. Calculations of probability characteristics of a multiline system with repeated calls, Moscow University Computational Mathematics and Cybernetics 1, 43–49] and Neuts and Rao [Neuts, M.F., Rao, B.M., 1990. Numerical investigation of a multiserver retrial model, Queueing Systems 7, 169–190]. Moreover, we develop stable recursive schemes for the computation of the busy period moments. The corresponding distributions for the total number of customers served during a busy period are also studied. Several numerical results illustrate the efficiency of the methods and reveal interesting facts concerning the behavior of the M / M / c retrial queue.

On The Single Server Retrial Queue With Balking

We study the maximum number of infected individuals observed during an epidemic for a Susceptible-Infected-Susceptible (SIS) model which corresponds to a birth-death process with an absorbing state. We develop computational schemes for the corresponding distributions in a transient regime and till absorption. Moreover, we study the distribution of the current number of infected individuals given that the maximum number during the epidemic has not exceeded a given threshold. In this sense, some quasi-stationary distributions of a related process are also discussed.

Algorithmic Analysis of the Maximum Queue Length in a Busy Period for the M/M/c Retrial Queue

Abstract We are concerned with the M/G/1 retrial queue with balking. The ergodicity condition is first investigated making use of classical mean drift criteria. The limiting distribution of the number of customers in the system is determined with the help of a recursive approach based on the theory of regenerative processes. Many closed form expressions are obtained when we reduce to the M/M/1 queue for some representative balking policies.

On the number of customers served in the M/G/1 retrial queue: first moments and maximum entropy approach

This paper deals with the maximum number of customers in orbit (and in the system) during a busy period for the M/M/c retrial queue. Determining the distribution for the maximum number of customers in orbit is reduced to computation of certain absorption probabilities. By reducing to the single-server case we arrive at a closed analytic formula. For the multi-server case we develop an efficient algorithmic procedure for computation of this distribution by exploiting the special block-tridiagonal structure of the system. Numerical results illustrate the efficiency of the method and reveal interesting facts concerning the behavior of the M/M/c retrial queue.