466 research outputs found
Large closed queueing networks in semi-Markov environment and its application
The paper studies closed queueing networks containing a server station and
client stations. The server station is an infinite server queueing system,
and client stations are single-server queueing systems with autonomous service,
i.e. every client station serves customers (units) only at random instants
generated by a strictly stationary and ergodic sequence of random variables.
The total number of units in the network is . The expected times between
departures in client stations are . After a service completion
in the server station, a unit is transmitted to the th client station with
probability , and being processed in the th client
station, the unit returns to the server station. The network is assumed to be
in a semi-Markov environment. A semi-Markov environment is defined by a finite
or countable infinite Markov chain and by sequences of independent and
identically distributed random variables. Then the routing probabilities
and transmission rates (which are expressed via
parameters of the network) depend on a Markov state of the environment. The
paper studies the queue-length processes in client stations of this network and
is aimed to the analysis of performance measures associated with this network.
The questions risen in this paper have immediate relation to quality control of
complex telecommunication networks, and the obtained results are expected to
lead to the solutions to many practical problems of this area of research.Comment: 35 pages, 1 figure, 12pt, accepted: Acta Appl. Mat
Coupled queues with customer impatience
Motivated by assembly processes, we consider a Markovian queueing system with multiple coupled queues and customer impatience. Coupling means that departures from all constituent queues are synchronised and that service is interrupted whenever any of the queues is empty and only resumes when all queues are non-empty again. Even under Markovian assumptions, the state space grows exponentially with the number of queues involved. To cope with this inherent state space explosion problem, we investigate performance by means of two numerical approximation techniques based on series expansions, as well as by deriving the fluid limit. In addition, we provide closed-form expressions for the first terms in the series expansion of the mean queue content for the symmetric coupled queueing system. By an extensive set of numerical experiments, we show that the approximation methods complement each other, each one being accurate in a particular subset of the parameter space. (C) 2017 Elsevier B.V. All rights reserved
EUROPEAN CONFERENCE ON QUEUEING THEORY 2016
International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"
The total capacity of customers in the MMPP/GI/∞ queueing system
In the paper, the infinite-server queueing system with a random capacity of customers is considered. In this system, the total capacity of customers is analysed by means of the asymptotic analysis method with high-rate Markov Modulated Poisson Process arrivals. It is obtained that the stationary probability distribution of the total customer capacity can be approximated by the Gaussian distribution. Parameters of the approximation is also derived in the pape
Pseudo steady-state period in non-stationary infinite-server queue with state dependent arrival intensity
An infinite-server queueing model with state-dependent arrival process and exponential distribution of service time is analyzed. It is assumed that the difference between the value of the arrival rate and total service rate becomes positive starting from a certain value of the number of customers in the system. In this paper, time until reaching this value by the number of customers in the system is called the pseudo steady-state period (PSSP). Distribution of duration of PSSP, its raw moments and its simple approximation under a certain scaling of the number of customers in the system are analyzed. Novelty of the considered problem consists of an arbitrary dependence of the rate of customer arrival on the current number of customers in the system and analysis of time until reaching from below a certain level by the number of customers in the system. The relevant existing papers focus on the analysis of time interval since exceeding a certain level until the number of customers goes down to this level (congestion period). Our main contribution consists of the derivation of a simple approximation of the considered time distribution by the exponential distribution. Numerical examples are presented, which confirm good quality of the proposed approximation
The effective bandwidth problem revisited
The paper studies a single-server queueing system with autonomous service and
priority classes. Arrival and departure processes are governed by marked
point processes. There are buffers corresponding to priority classes,
and upon arrival a unit of the th priority class occupies a place in the
th buffer. Let , denote the quota for the total
th buffer content. The values are assumed to be large, and
queueing systems both with finite and infinite buffers are studied. In the case
of a system with finite buffers, the values characterize buffer
capacities.
The paper discusses a circle of problems related to optimization of
performance measures associated with overflowing the quota of buffer contents
in particular buffers models. Our approach to this problem is new, and the
presentation of our results is simple and clear for real applications.Comment: 29 pages, 11pt, Final version, that will be published as is in
Stochastic Model
The NxD-BMAP/G/1 queueing model : queue contents and delay analysis
We consider a single-server discrete-time queueing system with N sources, where each source is modelled as a correlated Markovian customer arrival process, and the customer service times are generally distributed. We focus on the analysis of the number of customers in the queue, the amount of work in the queue, and the customer delay. For each of these quantities, we will derive an expression for their steady-state probability generating function, and from these results, we derive closed-form expressions for key performance measures such as their mean value, variance, and tail distribution. A lot of emphasis is put on finding closed-form expressions for these quantities that reduce all numerical calculations to an absolute minimum
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