569 research outputs found
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 TakĂĄcs Award for outstanding PhD thesis on "Queueing Theory and its Applications"
Scaling limits for infinite-server systems in a random environment
This paper studies the effect of an overdispersed arrival process on the
performance of an infinite-server system. In our setup, a random environment is
modeled by drawing an arrival rate from a given distribution every
time units, yielding an i.i.d. sequence of arrival rates
. Applying a martingale central limit theorem, we
obtain a functional central limit theorem for the scaled queue length process.
We proceed to large deviations and derive the logarithmic asymptotics of the
queue length's tail probabilities. As it turns out, in a rapidly changing
environment (i.e., is small relative to ) the overdispersion
of the arrival process hardly affects system behavior, whereas in a slowly
changing random environment it is fundamentally different; this general finding
applies to both the central limit and the large deviations regime. We extend
our results to the setting where each arrival creates a job in multiple
infinite-server queues
Strong approximations for time-varying infinite-server queues with non-renewal arrival and service processes
In real stochastic systems, the arrival and service processes may not be renewal processes. For example, in many telecommunication systems such as internet traffic where data traffic is bursty, the sequence of inter-arrival times and service times are often correlated and dependent. One way to model this non-renewal behavior is to use Markovian Arrival Processes (MAPs) and Markovian Service Processes (MSPs). MAPs and MSPs allow for inter-arrival and service times to be dependent, while providing the analytical tractability of simple Markov processes. To this end, we prove fluid and diffusion limits for MAP(t)/MSPt/ queues by constructing a new Poisson process representation for the queueing dynamics and leveraging strong approximations for Poisson processes. As a result, the fluid and diffusion limit theorems illuminate how the dependence structure of the arrival or service processes can affect the sample path behavior of the queueing process. Finally, our Poisson representation for MAPs and MSPs is useful for simulation purposes and may be of independent interest.111sciescopu
Asymptotic analysis by the saddle point method of the Anick-Mitra-Sondhi model
We consider a fluid queue where the input process consists of N identical
sources that turn on and off at exponential waiting times. The server works at
the constant rate c and an on source generates fluid at unit rate. This model
was first formulated and analyzed by Anick, Mitra and Sondhi. We obtain an
alternate representation of the joint steady state distribution of the buffer
content and the number of on sources. This is given as a contour integral that
we then analyze for large N. We give detailed asymptotic results for the joint
distribution, as well as the associated marginal and conditional distributions.
In particular, simple conditional limits laws are obtained. These shows how the
buffer content behaves conditioned on the number of active sources and vice
versa. Numerical comparisons show that our asymptotic results are very accurate
even for N=20
An acceleration simulation method for power law priority traffic
A method for accelerated simulation for simulated self-similar processes is proposed. This technique simplifies
the simulation model and improves the efficiency by using excess packets instead of packet-by-packet source traffic for a FIFO and non-FIFO buffer scheduler. In this research is focusing on developing an equivalent model of the conventional packet buffer that can produce an output analysis (which in this case will be the steady state probability) much faster. This acceleration simulation method is a further development of the Traffic Aggregation technique, which had previously been applied to FIFO buffers only and applies the Generalized Ballot Theorem to calculate the waiting time for the low priority traffic (combined with prior work on traffic aggregation). This hybrid method is shown to provide a significant reduction in the process time, while maintaining queuing behavior in the buffer that is highly accurate when compared to results from a conventional simulatio
On the modelling and performance measurement of service networks with heterogeneous customers
Service networks are common throughout the modern world, yet understanding how their individual services effect each other and contribute to overall system performance can be difficult. An important metric in these systems is the quality of service. This is an often overlooked measure when modelling and relates to how customers are affected by a service. Presented is a novel perspective for evaluating the performance of multi-class queueing networks through a combination of operational performance and service qualityâdenoted the âflow of outcomesâ. Here, quality is quantified by customers moving between or remaining in classes as a result of receiving service or lacking service. Importantly, each class may have different flow parameters, hence the positive/negative impact of service quality on the systemâs operational performance is captured. A fluidâdiffusion approximation for networks of stochastic queues is used since it allows for several complex flow dynamics: the sequential use of multiple services; abandonment and possible rejoin; reuse of the same service; multiple customers classes; and, class and time dependent parameters. The scalability of the approach is a significant benefit since, the modelled systems may be relatively large, and the included flow dynamics may render the system analytically intractable or computationally burdensome. Under the right conditions, this method provides a framework for quickly modelling large time-dependent systems. This combination of computational speed and the âflow of outcomesâ provides new avenues for the analysis of multi-class service networks where both service quality and operational efficiency interact
Optimal control of single-server fluid networks
We consider a stochastic single server fluid network with both a discounted reward and a cost structure. It can be shown that the optimal policy is a priority index policy. The indices coincide with the optimal indices in a Semi-Markovian Klimov problem. Several special cases like single server re-entrant fluid lines are considered. The approach we use is based on sample path arguments and Pontryagins maximum principle
Dynamic Service Rate Control for a Single Server Queue with Markov Modulated Arrivals
We consider the problem of service rate control of a single server queueing
system with a finite-state Markov-modulated Poisson arrival process. We show
that the optimal service rate is non-decreasing in the number of customers in
the system; higher congestion rates warrant higher service rates. On the
contrary, however, we show that the optimal service rate is not necessarily
monotone in the current arrival rate. If the modulating process satisfies a
stochastic monotonicity property the monotonicity is recovered. We examine
several heuristics and show where heuristics are reasonable substitutes for the
optimal control. None of the heuristics perform well in all the regimes.
Secondly, we discuss when the Markov-modulated Poisson process with service
rate control can act as a heuristic itself to approximate the control of a
system with a periodic non-homogeneous Poisson arrival process. Not only is the
current model of interest in the control of Internet or mobile networks with
bursty traffic, but it is also useful in providing a tractable alternative for
the control of service centers with non-stationary arrival rates.Comment: 32 Pages, 7 Figure
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