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180
Exact overflow asymptotics for queues with many Gaussian inputs
 J. APPL. PROBAB
, 2002
"... In this paper we consider a queue fed by a large number n of independent continuoustime Gaussian processes with stationary increments. After scaling the buffer exceedance threshold B and the (constant) service capacity C by then umber of sources (i.e., B nb and C nc), we present asymptoticall ..."
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Cited by 21 (6 self)
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In this paper we consider a queue fed by a large number n of independent continuoustime Gaussian processes with stationary increments. After scaling the buffer exceedance threshold B and the (constant) service capacity C by then umber of sources (i.e., B nb and C nc), we present asymptotically exact results for the probability that the buffer threshold is exceeded. We both consider the stationary overflow probability, and the (transient) probability of overflow at a finite time horizon T. We give detailed results on the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.
Convexity properties of loss and overflow functions
 Operations Research Letters
, 2003
"... We show that the fluid loss ratio in a fluid queue with finite buffer � and constant link capacity is always a jointly convex function of � and. This generalizes prior work [7] which shows convexity of the � � tradeoff for large number of i.i.d. multiplexed sources, using the large deviations rate ..."
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Cited by 13 (0 self)
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We show that the fluid loss ratio in a fluid queue with finite buffer � and constant link capacity is always a jointly convex function of � and. This generalizes prior work [7] which shows convexity of the � � tradeoff for large number of i.i.d. multiplexed sources, using the large deviations rate function as approximation for fluid loss. Our approach also leads to a simpler proof of the prior result, and provides a stronger basis for optimal measurementbased control of resource allocation in shared resource systems.
Overflow Behavior in Queues with Many LongTailed Inputs
 ADVANCES IN APPLIED PROBABILITY
, 1999
"... We consider a fluid queue fed by a superposition of n homogeneous onoff sources with generally distributed on and offperiods. We scale buffer space B and link rate C by n, such that we get nb and nc, respectively. Then we let n grow large. In this regime, the overflow probability decays exponenti ..."
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Cited by 16 (7 self)
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We consider a fluid queue fed by a superposition of n homogeneous onoff sources with generally distributed on and offperiods. We scale buffer space B and link rate C by n, such that we get nb and nc, respectively. Then we let n grow large. In this regime, the overflow probability decays exponentially in the number of sources n; we specifically examine the situation in which also b is large. We explicitly compute asymptotics for the case in which the onperiods have a subexponential distribution, e.g., Pareto, Lognormal, or Weibull. We provide a detailed interpretation of our results. Crucial is the shape of the function v(t) := log P(A* > t) for large t, A* being the residual onperiod. If v(·) is slowly varying (e.g., Pareto, Lognormal), then, during the trajectory to overflow, the input rate will only slightly exceed the link rate. Consequently, the buffer will fill `slowly', and the typical time to overflow will be `more than linear' in the buffer size. In contrast, if v(·) ...
Analysis and efficient simulation of queueing models of telecommunication systems
, 2000
"... ter verkrijging van de graad van doctor aan de Universiteit Twente, op gezag van de rector magnificus, prof. dr. F.A. van Vught, volgens besluit van het College voor Promoties in het openbaar te verdedigen ..."
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Cited by 23 (7 self)
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ter verkrijging van de graad van doctor aan de Universiteit Twente, op gezag van de rector magnificus, prof. dr. F.A. van Vught, volgens besluit van het College voor Promoties in het openbaar te verdedigen
Optimal Trajectory to Overflow in a Queue Fed By a Large Number of Sources
 Queueing Systems
, 1998
"... We analyse the deviant behavior of a queue fed by a large number of traffic streams. In particular, we explicitly give the most likely trajectory (or `optimal path') to buffer overflow, by applying large deviations techniques. This is done for a broad class of sources, consisting of Markov flui ..."
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Cited by 17 (8 self)
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We analyse the deviant behavior of a queue fed by a large number of traffic streams. In particular, we explicitly give the most likely trajectory (or `optimal path') to buffer overflow, by applying large deviations techniques. This is done for a broad class of sources, consisting of Markov fluid sources and periodic sources. Apart from a number of ramifications of this result, we present guidelines for the numerical evaluation of the optimal path.
Multiplexing Regulated Traffic Streams: Design and Performance
, 2001
"... The main network solutions for supporting QoS rely on traffic policing (conditioning, shaping). In particular, for IP networks the IETF has developed Intserv (individual flows regulated) and Diffserv (only aggregates regulated). The regulator proposed could be based on the (dual) leakybucket mechan ..."
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Cited by 15 (0 self)
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The main network solutions for supporting QoS rely on traffic policing (conditioning, shaping). In particular, for IP networks the IETF has developed Intserv (individual flows regulated) and Diffserv (only aggregates regulated). The regulator proposed could be based on the (dual) leakybucket mechanism. This explains the interest in network element performance (loss, delay) for leakybucket regulated traffic. This paper describes a novel approach to the above problem. Explicitly using the correlation structure of the sources' traffic, we derive approximations for both small and large buffers. Importantly, for small (large) buffers the shortterm (longterm) correlations are dominant. The large buffer result decomposes the traffic stream in a stream of constant rate and a periodic impulse stream, allowing direct application of the Brownian bridge approximation. Combining the small and large buffer results by a concave majorization, we propose a simple, fast and accurate technique to statistically multiplex homogeneous regulated sources. To address heterogeneous inputs, we present similarly efficient techniques to evaluate the performance of multiple classes of traffic, each with distinct characteristics and QoS requirements. These techniques, applicable under more general conditions, are based on optimal resource (bandwidth and buffer) partitioning. They can also be directly applied to set GPS (Generalized Processor Sharing) weights and buffer thresholds in a shared resource system.
E[D(t)]
, 2012
"... Some performance measures of interest The law of {D(t), t ≥ 0} E[D(t)], Var ..."
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Some performance measures of interest The law of {D(t), t ≥ 0} E[D(t)], Var
A largedeviations analysis of the GI/GI/1 SRPT queue. Queueing Systems: Theory and Applications
, 2006
"... We consider a GI=GI=1 queue with the shortest remaining processing time discipline (SRPT) and lighttailed service times. Our interest is focused on the tail behavior of the sojourntime distribution. We obtain a general expression for its largedeviations decay rate. The value of this decay rate cr ..."
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Cited by 14 (7 self)
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We consider a GI=GI=1 queue with the shortest remaining processing time discipline (SRPT) and lighttailed service times. Our interest is focused on the tail behavior of the sojourntime distribution. We obtain a general expression for its largedeviations decay rate. The value of this decay rate critically depends on whether there is mass in the endpoint of the servicetime distribution or not. An auxiliary priority queue, for which we obtain some new results, plays an important role in our analysis. We apply our SRPT results to compare SRPT with FIFO from a largedeviations point of view.
Results 11  20
of
180