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This paper studies a fluid queue with coupled input and output. Flows arrive according to a Poisson process, and when n flows are present, each of them transmits traffic into the queue at a rate c/(n+1), where the remaining c/(n+1) is used to serve the queue. We assume exponentially distributed flow sizes, so that the queue under consideration can
be regarded as a system with Markov fluid input. The rationale behind studying this queue lies in ad hoc networks: bottleneck
links have roughly this type of sharing policy. We consider four performance metrics: (i) the stationary workload of the queue,
(ii) the queueing delay, i.e., the delay of a ‘packet’ (a fluid particle) that arrives at the queue at an arbitrary point
in time, (iii) the flow transfer delay, i.e., the time elapsed between arrival of a flow and the epoch that all its traffic
has been put into the queue, and (iv) the sojourn time, i.e., the flow transfer time increased by the time it takes before
the last fluid particle of the flow is served. For each of these random variables we compute the Laplace transform. The corresponding
tail probabilities decay exponentially, as is shown by a large-deviations analysis.
F. Roijers’ work has been carried out partly in the SENTER-NOVEM funded project Easy Wireless. 相似文献
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Hans van den Berg Michel Mandjes Rudesindo Núñez-Queija 《Operations Research Letters》2007,35(3):297-307
We study a processor-sharing model in which users choose between a high- and a low-priority service, based on their utility functions and prices charged by the service provider. The latter aims at revenue maximization. The model is motivated by file transmissions in data networks with distributed congestion control. 相似文献
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This short communication considers the workload process of a queue operating in slotted time, focusing on the (multivariate) distribution of the workloads at different points in time. In a many-sources framework exact asymptotics are determined, relying on large-deviations results for the sample means of multivariate random variables. 相似文献
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R. Malhotra M. R. H. Mandjes W. R. W. Scheinhardt J. L. van den Berg 《Mathematical Methods of Operations Research》2009,70(1):149-169
Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper
we present and analyze a fluid queue with a feedback-based traffic rate adaptation scheme which uses two thresholds. The higher
threshold B
1 is used to signal the beginning of congestion while the lower threshold B
2 signals the end of congestion. These two parameters together allow to make the trade-off between maximizing throughput performance
and minimizing delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the
traffic source. In our model the input source can behave like either of two Markov fluid processes. The first applies as long
as the upper threshold B
1 has not been hit from below. As soon as that happens, the traffic source adapts and switches to the second process, until
B
2 (smaller than B
1) is hit from above. We analyze the model by setting up the Kolmogorov forward equations, then solving the corresponding balance
equations using a spectral expansion, and finally identifying sufficient constraints to solve for the unknowns in the solution.
In particular, our analysis yields expressions for the stationary distribution of the buffer occupancy, the buffer delay distribution,
and the throughput. 相似文献
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This paper considers a Markov fluid queue, focusing on the correlation function of the stationary workload process. A simulation-based computation technique is proposed, which relies on a coupling idea. Then an upper bound on the variance of the resulting estimator is given, which reveals how the coupling time and the busy period of the Markov fluid queue affect the performance of the computation procedure. A numerical assessment, in which we compare the proposed technique with naive simulation, gives an indication of the achievable efficiency gain in various scenarios. 相似文献
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This paper considers queues with server vacations, but departs from the traditional setting in two ways: (i) the queueing
model is driven by Lévy processes rather than just compound Poisson processes; (ii) the vacation lengths depend on the length
of the server’s preceding busy period. Regarding the former point: the Lévy process active during the busy period is assumed
to have no negative jumps, whereas the Lévy process active during the vacation is a subordinator. Regarding the latter point:
where in a previous study (Boxma et al. in Probab. Eng. Inf. Sci. 22:537–555, 2008) the durations of the vacations were positively correlated with the length of the preceding busy period, we now introduce
a dependence structure that may give rise to both positive and negative correlations. We analyze the steady-state workload of the resulting queueing (or: storage) system, by first considering
the queue at embedded epochs (viz. the beginnings of busy periods). We show that this embedded process does not always have
a proper stationary distribution, due to the fact that there may occur an infinite number of busy-vacation cycles in a finite
time interval; we specify conditions under which the embedded process is recurrent. Fortunately, irrespective of whether the
embedded process has a stationary distribution, the steady-state workload of the continuous-time storage process can be determined. In addition, a number of ramifications are presented. The theory is illustrated by several examples. 相似文献
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In service systems, in order to balance the server’s idle times and the customers’ waiting times, one may fix the arrival times of the customers beforehand in an appointment schedule. We propose a procedure for determining appointment schedules in such a D/G/1-type of system by sequentially minimizing the per-customer expected loss. Our approach provides schedules for any convex loss function; for the practically relevant cases of the quadratic and absolute value loss functions appealing closed-form results are derived. Importantly, our approach does not impose any conditions on the service time distribution; it is even allowed that the customers’ service times have different distributions. 相似文献