Results 1  10
of
23
Reducedload equivalence and induced burstiness in GPS queues with longtailed traffic flows
 Theory Appl
, 2000
"... ..."
Exact asymptotics for fluid queues fed by multiple heavytailed onoff flows
 Ann. Appl. Probab
"... We consider a fluid queue fed by multiple On–Off flows with heavytailed (regularly varying) On periods. Under fairly mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a reduced system. The reduced system consists of a “dominant ” subset of the flows, ..."
Abstract

Cited by 18 (9 self)
 Add to MetaCart
We consider a fluid queue fed by multiple On–Off flows with heavytailed (regularly varying) On periods. Under fairly mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a reduced system. The reduced system consists of a “dominant ” subset of the flows, with the original service rate subtracted by the mean rate of the other flows. We describe how a dominant set may be determined from a simple knapsack formulation. The dominant set consists of a “minimally critical ” set of On– Off flows with regularly varying On periods. In case the dominant set contains just a single On–Off flow, the exact asymptotics for the reduced system follow from known results. For the case of several On–Off flows, we exploit a powerful intuitive argument to obtain the exact asymptotics. Combined with the reducedload equivalence, the results for the reduced system provide a characterization of the tail of the workload distribution for a wide range of traffic scenarios.
Capacity Regions for Network Multiplexers with HeavyTailed Fluid OnOff Sources
, 2001
"... Consider a network multiplexer with a finite buffer fed by a superposition of independent heterogeneous OnOff sources. An OnOff source consists of a sequence of alternating independent activity and silence periods. During its activity period a source produces fluid with constant rate. For this sys ..."
Abstract

Cited by 15 (6 self)
 Add to MetaCart
Consider a network multiplexer with a finite buffer fed by a superposition of independent heterogeneous OnOff sources. An OnOff source consists of a sequence of alternating independent activity and silence periods. During its activity period a source produces fluid with constant rate. For this system, under the assumption that the residual activity periods are intermediately regularly varying, we derive explicit and asymptotically exact formulas for approximating the stationary overflow probability and loss rate. The derived asymptotic formulas, in addition to their analytical tractability, exhibit excellent quantitative accuracy, which is illustrated by a number of simulation experiments. We demonstrate through examples how these results can be used for efficient computing of capacity regions for network switching elements. Furthermore, the results provide important insight into qualitative tradeoffs between the overflow probability, offered traffic load, available capacity, and buffer space. Overall, they provide a new set of tools for designing and provisioning of networks with heavytailed traffic streams. KeywordsNetwork multiplexer, Finite buffer fluid queue, OnOff process, Heavytailed distributions, Subexponential distributions, Longrange dependence I.
Asymptotic Loss Probability in a Finite Buffer Fluid Queue with Heterogeneous HeavyTailed OnOff Processes
, 2000
"... Consider a fluid queue with a finite buffer B and capacity c fed by a superposition of N independent OnOff processes. An OnOff process consists of a sequence of alternating independent activity and silence periods. Successive activity, as well as silence, periods are identically distributed. The p ..."
Abstract

Cited by 13 (5 self)
 Add to MetaCart
Consider a fluid queue with a finite buffer B and capacity c fed by a superposition of N independent OnOff processes. An OnOff process consists of a sequence of alternating independent activity and silence periods. Successive activity, as well as silence, periods are identically distributed. The process is active with probability p on and during its activity period produces fluid with constant rate r. For this queueing system, under the assumption that the residual activity periods are intermediately regularly varying, we derive explicit and asymptotically exact formulas for approximating the stationary loss probability and loss rate. In the case of homogeneous sources with residual activity periods equal in distribution to on r , the queue overflow probability is asymptotically, as B !1, equal to P[Q B = B] = ` N k 0 ' p k 0 on P on r ? B k 0 (r \Gamma ae) +N ae \Gamma c k 0 (1 + o(1)); where ae = rp on , N ae ! c and k 0 is the smallest integer greater than (c...
Steady State Distribution Of The Buffer Content For M/G/infinity Input Fluid Queues
, 1999
"... . We consider a fluid queue with ON periods arriving according to a Poisson process and having a longtailed distribution. This queue has long range dependence, and we compute the asymptotic behavior of the steady state distribution of the buffer content. The tail of this distribution is much heavi ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
. We consider a fluid queue with ON periods arriving according to a Poisson process and having a longtailed distribution. This queue has long range dependence, and we compute the asymptotic behavior of the steady state distribution of the buffer content. The tail of this distribution is much heavier than the tail of the buffer content distribution of a queue which does not possess long range dependence and which has light tailed ON periods and the same traffic intensity. 1. Introduction and preliminaries We consider a model of a network server (multiplexer) defined as follows. Sessions arrive to the server according to a Poisson process with rate ? 0. Each session lasts a random length of time with distribution F that has a finite mean . The lengths of different sessions are independent of each other and of the Poisson arrival process. A session generates work or traffic or fluid at unit rate, commonly measured in some units of network traffic, e.g. packets; the work that cannot be ...
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 ..."
Abstract

Cited by 11 (7 self)
 Add to MetaCart
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(·) ...
Tail asymptotics for discriminatory processorsharing queues with heavytailed service requirements
 Perf. Eval
, 2005
"... We derive the sojourn time asymptotics for a multiclass G/G/1 queue with regularly varying service requirements operating under the Discriminatory ProcessorSharing (DPS) discipline. DPS provides a natural approach for modelling the flowlevel performance of differentiated bandwidthsharing mechanis ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
We derive the sojourn time asymptotics for a multiclass G/G/1 queue with regularly varying service requirements operating under the Discriminatory ProcessorSharing (DPS) discipline. DPS provides a natural approach for modelling the flowlevel performance of differentiated bandwidthsharing mechanisms. Under certain assumptions, we prove that the service requirement and sojourn time of a given class have similar tail behaviour, independent of the specific values of the DPS weights. As a byproduct, we obtain an extension of the tail equivalence for ordinary ProcessorSharing (PS) queues to nonPoisson arrivals. The results suggest that DPS offers a potential instrument for effectuating preferential treatment to highpriority classes, without inflicting excessive delays on lowpriority classes. To obtain the asymptotics, we develop a novel method which only involves information of the workload process and does not require any knowledge of the steadystate queue length distribution. In particular, the proof method brings sufficient strength to extend the results to scenarios with a timevaring service capacity.
A Reducedload Equivalence for Generalised Processor Sharing Networks with Heavytailed Input Flows
 Queueing Systems
, 2000
"... We consider networks where traffic is served according to the Generalised Processor Sharing (GPS) principle. GPSbased scheduling algorithms are considered important for providing differentiated quality of service in integratedservices networks. We are interested in the workload of a particular flo ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
We consider networks where traffic is served according to the Generalised Processor Sharing (GPS) principle. GPSbased scheduling algorithms are considered important for providing differentiated quality of service in integratedservices networks. We are interested in the workload of a particular flow i at the bottleneck node on its path. Flow i is assumed to have longtailed traffic characteristics. We distinguish between two traffic scenarios, (i) flow i generates instantaneous traffic bursts and (ii) flow i generates traffic according to an on/off process. In addition, we consider two configurations of feedforward networks. First we focus on the situation where other flows join the path of flow i. Then we extend the model by adding flows which can branch off at any node, with cross traffic as a special case. We prove that under certain conditions the tail behaviour of the workload distribution of flow i is equivalent to that in a twonode tandem network where flow i is served in is...
Two coupled queues with heterogeneous traffic
 Proc. ITC17
, 2001
"... We consider a system with two heterogeneous traffic classes, one having lighttailed characteristics, the other one exhibiting heavytailed properties. When both classes are backlogged, the two corresponding queues are each served at a certain nominal rate. However, when one queue empties, the serv ..."
Abstract

Cited by 6 (6 self)
 Add to MetaCart
We consider a system with two heterogeneous traffic classes, one having lighttailed characteristics, the other one exhibiting heavytailed properties. When both classes are backlogged, the two corresponding queues are each served at a certain nominal rate. However, when one queue empties, the service rate for the other class increases. This dynamic sharing of surplus service capacity is reminiscent of the Generalized Processor Sharing (GPS) discipline. GPSbased scheduling algorithms, such as Weighted Fair Queueing, provide a candidate implementation mechanism for achieving differentiated QualityofService in a DiffServ architecture.
We characterize the asymptotic workload behavior of both traffic classes. The tail of the workload distribution of the heavytailed class is asymptotically equivalent to that of the heavytailed class in isolation  but with its nominal service rate inflated by the slack capacity of the lighttailed class. For the lighttailed class, we show a sharp dichotomy in the qualitative behavior, depending on whether its load exceeds its nominal service rate or not. In underload scenarios, the tail of its workload distribution is equivalent to that of the lighttailed class in isolation, multiplied with a certain prefactor. The prefactor represents the probability that the heavytailed class is backlogged long enough for the lighttailed class to build up a large workload. This provides a measure for the extent to which the lighttailed class benefits from sharing surplus capacity with the heavytailed class. In contrast, in overload situations, the lighttailed class is adversely affected by the heavytailed class, and inherits its traffic characteristics.
Perturbation analysis of a variable M/M/1 queue: a probabilistic approach, submitted for publication
 Advances in Applied Probability
, 2005
"... Abstract. Motivated by the problem of the coexistence on transmission links of telecommunication networks of elastic and unresponsive traffic, we study in this paper the impact on the busy period of an M/M/1 queue of a small perturbation in the server rate. The perturbation depends upon an independe ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
Abstract. Motivated by the problem of the coexistence on transmission links of telecommunication networks of elastic and unresponsive traffic, we study in this paper the impact on the busy period of an M/M/1 queue of a small perturbation in the server rate. The perturbation depends upon an independent stationary process (X(t)) and is quantified by means of a parameter ε ≪ 1. We specifically compute the two first terms of the power series expansion in ε of the mean value of the busy period duration. This allows us to study the validity of the Reduced Service Rate (RSR) approximation, which consists in comparing the perturbated M/M/1 queue with the M/M/1 queue where the service rate is constant and equal to the mean value of the perturbation. For the first term of the expansion, the two systems are equivalent. For the second term, the situation is more complex and it is shown that the correlations of