A state‐dependent Markov‐modulated mechanism for generating events and stochastic models

In this paper, we introduce a versatile block‐structured state‐dependent event (BSDE) approach that provides a methodological tool to construct non‐homogeneous Markov‐modulated stochastic models. Alternatively, the BSDE approach can be used to construct even a part (e.g. the arrival process) of the model. To illustrate the usefulness of the BSDE approach, several arrival patterns as well as queueing and epidemic models are considered. In particular, we deal with a state‐dependent quasi‐birth‐and‐death process that gives a constructive generalization of the scalar birth‐and‐death process and the homogeneous quasi‐birth‐and‐death process. Copyright © 2009 John Wiley & Sons, Ltd.     

A heuristic approach for deriving the priority vector in AHP

This paper proposes an approach for deriving the priority vector from an inconsistent pair-wise comparison matrix through the nearest consistent matrix and experts judgments, which enables balancing the consistency and experts judgments. The developed algorithm for achieving a nearest consistent matrix is based on a logarithmic transformation of the pair-wise comparison matrix, and follows an iterative feedback process that identifies an acceptable level of consistency while complying with experts preferences. Three numerical examples are examined to illustrate applications and advantages of the developed approach.     

A semi-preemptive priority scheduling discipline: Performance analysis

In this paper, we present an in-depth analytical study of a semi-preemptive priority scheduling discipline. This discipline eliminates the deficits of both the full- and non-preemptive versions. Under the non-preemptive category, in particular, higher-priority customers may have to wait even when the service of a lower-priority customer has just started, while under the full-preemptive discipline, the almost completed service of a lower-priority customer may be interrupted due to the arrival of higher-priority customers, possibly causing a large extra delay. For fixed low-priority service times, the semi-preemptive priority scheduling discipline shows a performance gain of up to 6% compared to the full- and non-preemptive versions.     

Some New Results for Departure Process in the M X /G/1 Queueing System with a Single Vacation and Exhaustive Service

A batch arrival queueing system with a single vacation between two successive busy periods and with exhaustive service is considered.

The departure process h(t) is studied first on a single vacation cycle. The approach based on renewal theory is applied to obtain results in the general case. In particular, the explicit representation for the generating function of Laplace transform of the probability function of h(t) is derived. All formulae are written in terms of input parameters of the system and factors of a certain canonical factorization of Wiener–Hopf type. A numerical approach to results is discussed as well.     

Tandem queueing system with infinite and finite intermediate buffers and generalized phase-type service time distribution

A tandem queueing system with infinite and finite intermediate buffers, heterogeneous customers and generalized phase-type service time distribution at the second stage is investigated. The first stage of the tandem has a finite number of servers without buffer. The second stage consists of an infinite and a finite buffers and a finite number of servers. The arrival flow of customers is described by a Marked Markovian arrival process. Type 1 customers arrive to the first stage while type 2 customers arrive to the second stage directly. The service time at the first stage has an exponential distribution. The service times of type 1 and type 2 customers at the second stage have a phase-type distribution with different parameters. During a waiting period in the intermediate buffer, type 1 customers can be impatient and leave the system. The ergodicity condition and the steady-state distribution of the system states are analyzed. Some key performance measures are calculated. The Laplace–Stieltjes transform of the sojourn time distribution of type 2 customers is derived. Numerical examples are presented.     

Upper bound for the decay rate of the joint queue-length distribution in a two-node Markovian queueing system

This paper studies the geometric decay property of the joint queue-length distribution {p(n ₁,n ₂)} of a two-node Markovian queueing system in the steady state. For arbitrarily given positive integers c ₁,c ₂,d ₁ and d ₂, an upper bound of the decay rate is derived in the sense

A simulation model for determining variable worker requirements in a service operation with time-dependent customer demand

In a service operation where worker requirements have to be determined for short scheduling time periods with nonstationary customer demand, the assumptions necessary for applying steady-state solutions to elementary queueing models are usually violated. This paper describes a simulation study of the behavior of such a service operation. The results are compared with the steady-state solutions to a queueing model where individual scheduling time periods are assumed to be independent. It is found that if the system utilization is below a derived maximum value (based on a service level criterion), then the steady-state solutions are robust enough to explain the behavior of the system and can be used to schedule worker requirements.     

Multi-residue analysis and ultra-trace quantification of 36 priority substances from the European Water Framework Directive by GC-MS and LC-FLD-MS/MS in surface waters

A multi residue analysis was developed for screening, quantification and confirmation of 36 priority organic compounds included in the 2000/60/EC European Water Framework Directive. The compounds analyzed included 19 pesticides, 8 PAH, 5 endocrine-disruptors and 4 organochlorine compounds. The method was developed in three steps. First, automated off-line solid-phase extraction using Strata X cartridges was optimized to trap simultaneously the 36 studied compounds. Second, the more volatile compounds were analysed by gas chromatography coupled to mass spectrometry with electron impact ionisation in selected ion monitoring mode (SIM). Third, the last 20 compounds were detected and quantified, in one run, by liquid chromatography coupled to fluorescence detector and tandem mass spectrometry. The excellent selectivity and sensitivity allowed us satisfactory quantification and confirmation at levels as low as 0.2-67 ng L⁻¹ with recoveries between 59 and 105%. Such methodology was then applied to French surface waters: all the waters present organic contaminants, and their concentration varied according to the origin and nature of substances.