637 research outputs found
System-theoretical algorithmic solution to waiting times in semi-Markov queues
Cataloged from PDF version of article.Markov renewal processes with matrix-exponential semi-Markov kernels provide a
generic tool for modeling auto-correlated interarrival and service times in queueing
systems. In this paper, we study the steady-state actual waiting time distribution in an
infinite capacity single-server semi-Markov queue with the auto-correlation in interarrival
and service times modeled by Markov renewal processes with matrix-exponential kernels.
Our approach is based on the equivalence between the waiting time distribution of this
semi-Markov queue and the output of a linear feedback interconnection system. The
unknown parameters of the latter system need to be determined through the solution of
a SDC (Spectral-Divide-and-Conquer) problem for which we propose to use the ordered
Schur decomposition. This approach leads us to a completely matrix-analytical algorithm
to calculate the steady-state waiting time which has a matrix-exponential distribution.
Besides its unifying structure, the proposed algorithm is easy to implement and is
computationally efficient and stable. We validate the effectiveness and the generality of the proposed approach through numerical examples.
© 2009 Elsevier B.V. All rights reserve
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Performance modelling of wormhole-routed hypercubes with bursty traffice and finite buffers
An open queueing network model (QNM) is proposed for wormhole-routed hypercubes with finite
buffers and deterministic routing subject to a compound Poisson arrival process (CPP) with geometrically
distributed batches or, equivalently, a generalised exponential (GE) interarrival time distribution. The GE/G/1/K
queue and appropriate GE-type flow formulae are adopted, as cost-effective building blocks, in a queue-by-queue
decomposition of the entire network. Consequently, analytic expressions for the channel holding time, buffering
delay, contention blocking and mean message latency are determined. The validity of the analytic approximations
is demonstrated against results obtained through simulation experiments. Moreover, it is shown that the wormholerouted
hypercubes suffer progressive performance degradation with increasing traffic variability (burstiness)
Queues and risk processes with dependencies
We study the generalization of the G/G/1 queue obtained by relaxing the
assumption of independence between inter-arrival times and service
requirements. The analysis is carried out for the class of multivariate matrix
exponential distributions introduced in [12]. In this setting, we obtain the
steady state waiting time distribution and we show that the classical relation
between the steady state waiting time and the workload distributions re- mains
valid when the independence assumption is relaxed. We also prove duality
results with the ruin functions in an ordinary and a delayed ruin process.
These extend several known dualities between queueing and risk models in the
independent case. Finally we show that there exist stochastic order relations
between the waiting times under various instances of correlation
Estimation of a Simple Queuing System WithUnits-in-Service and Complete Data
Queuing theory may be useful for analyzing economic phenomena involving
count and duration data. We develop maximum likelihood estimators for the time-varying
parameters of a simple queuing system based on two kinds of data: complete interarrival
and service times (IST), and number of units in service (NIS). The IST estimator dominates
the NIS estimator, in terms of ease of implementation, bias, and variance. The
model is useful for many empirical applications in economics.m (t)/M (t)/8 queue, infinite server queue, time-varying parameters, Poisson stochasticprocess, duration data
Simulation study for the effect of dependencies in queueing systems
Few theoretical results have been obtained in the literature for the effects of dependencies between random variables on the performance of queueing systems. This thesis aims at investigating this issue via simulation. Several dependencies are studied in detail, including dependencies between interarrival times, between interarrival time and service time, between service times and dependencies between different stages in networks of queues. We define several classes of dependent random variables and study their correlation coefficients, then we apply them to single and multiple station service systems. Comparisons with the independent case, for which the explicit form solution are available, are made and characterized by figures. The main contribution of this thesis is that it disproves the monotonicity properties of effect of dependencies on system performance in both single and multiple service stations queueing systems. These results may be helpful in evaluating the performance of both telecommunication and manufacturing systems
On the statistical description of the inbound air traffic over Heathrow airport
We present a model to describe the inbound air traffic over a congested hub.
We show that this model gives a very accurate description of the traffic by the
comparison of our theoretical distribution of the queue with the actual
distribution observed over Heathrow airport. We discuss also the robustness of
our model
Content Based Status Updates
Consider a stream of status updates generated by a source, where each update
is of one of two types: high priority or ordinary (low priority). These updates
are to be transmitted through a network to a monitor. However, the transmission
policy of each packet depends on the type of stream it belongs to. For the low
priority stream, we analyze and compare the performances of two transmission
schemes: (i) Ordinary updates are served in a First-Come-First-Served (FCFS)
fashion, whereas, in (ii), the ordinary updates are transmitted according to an
M/G/1/1 with preemption policy. In both schemes, high priority updates are
transmitted according to an M/G/1/1 with preemption policy and receive
preferential treatment. An arriving priority update discards and replaces any
currently-in-service high priority update, and preempts (with eventual resume
for scheme (i)) any ordinary update. We model the arrival processes of the two
kinds of updates, in both schemes, as independent Poisson processes. For scheme
(i), we find the arrival and service rates under which the system is stable and
give closed-form expressions for average peak age and a lower bound on the
average age of the ordinary stream. For scheme (ii), we derive closed-form
expressions for the average age and average peak age of the high priority and
low priority streams. We finally show that, if the service time is
exponentially distributed, the M/M/1/1 with preemption policy leads to an
average age of the low priority stream higher than the one achieved using the
FCFS scheme. Therefore, the M/M//1/1 with preemption policy, when applied on
the low priority stream of updates and in the presence of a higher priority
scheme, is not anymore the optimal transmission policy from an age point of
view
Modeling Stochastic Lead Times in Multi-Echelon Systems
In many multi-echelon inventory systems, the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process that generates such lead times is usually not well defined, which is especially a problem for simulation modeling. In this paper, we use results from queuing theory to define a set of simple lead time processes guaranteeing that (a) orders do not cross and (b) prespecified means and variances of all lead times in the multiechelon system are attained
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