This paper is motivated by the increasing popularity of streaming media applications that are off... more This paper is motivated by the increasing popularity of streaming media applications that are offered via the Internet. Packet streams generated by media application servers are distorted due to variability in the available bandwidth; at the receiving end, a play-out buffer compensates for the distortion. We study the dynamics of this system in a queuing-theoretical setting, using fluid analysis. To this end, we consider a model in which a constant bit-rate (CBR) media application is streamed over an unreliable network. Our model consists of a tandem of two fluid queues. The first queue is a Markov Modulated fluid queue that models the network congestion, and the second queue represents the play-out buffer. For this model the distribution of the total amount of fluid in the congestion and play-out buffers corresponds to the distribution of the maximum attained level of the first buffer. We show that the distribution of the total amount of fluid converges to a Gumbel extreme value distribution. From this result, we derive a simple closed-form expression for the initial playout-buffer level that provides a probabilistic guarantee for undisturbed playback.
Allegra, G. and Bassi, L 14/.: Isomorphism in Synthetic Macromolecular Systems. Vol. 6, pp. 549-5... more Allegra, G. and Bassi, L 14/.: Isomorphism in Synthetic Macromolecular Systems. Vol. 6, pp. 549-574. Andrews, E. H. : Molecular Fracture in Polymers. Vol. 27, pp. 1-66. Anufrieva, E. V. and Gotlib, Yu. Ya. : Investigation of Polymers in Solution by Polarized Luminescence. Vol. 40, pp. 1-68. Apicella, A., Nicolais, L. and de Cataldis, C. : Characterization of the Morphological Fine Structure of Commercial Thermosetting Resins Through Hygrothermal Experiments. Vol. 66, pp. 189-208. Argon, A. S., Cohen, R. E., Gebizlioglu, O. S. and Schwier, C. : Crazing in Block Copolymers and Blends. Vol. 52/53, pp. 275-334 Arridge, R. C. and Barham, P. J.: Polymer Elasticity. Discrete and Continuum Models. Vol. 46, pp. 67-117. Aseeva, R. M., Zaikov, G. E.: Flammability of Polymeric Materials. Vol. 70, pp. 171-230. Ayrey, G.: The Use of Isotopes in Polymer Analysis. Vol. 6, pp. 128-148.
Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications, 2006
We show that different flavors of TCP may be viewed as implementations of age-based scheduling di... more We show that different flavors of TCP may be viewed as implementations of age-based scheduling disciplines. By parameterizing the scheduling disciplines of interest we are able to position variants of TCP in a wide spectrum having FCFS (First-Come First-Served) and LAS (Least Attained Service first) as extremal policies, and including PS (Processor Sharing) as an intermediate case. We argue that for highly loaded systems, providing a fair bandwidth allocation among all users is secondary to ensuring network stability. So as to isolate protocol fairness from congestion effects, we therefore focus on scenarios with infinite buffers. This way, asymmetries in capacity shares are the consequences of the protocol only, and not affected by the packet loss process. The model, however, is flexible enough to include finite buffers with random packet loss as a special case (for example to capture Active Queue Management). The results are helpful in studying fairness and performance concerned with transmission protocols in communication networks. For persistent HTTP connections we study the distributions of the transmission rates and the relative fairness index under various assumptions on the file size distributions and scheduling disciplines. For infinite file sizes, we show that protocols that increase priority more than linearly with the attained service asymptotically behave similar to FCFS. In contrast, protocols with at most linearly increasing (or even decreasing) priority, with TCP's Congestion Avoidance mechanism as the most prominent example, converge to PS scheduling (even in absence of losses). When the priority is exactly linear in the attained service, such as for Scalable TCP and TCP's Slow Start phase, the shares remain constant in between file initiations and completions. 1 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the Proceedings IEEE Infocom.
We consider a system with two heterogeneous traffic classes. The users from both classes randomly... more We consider a system with two heterogeneous traffic classes. The users from both classes randomly generate service requests, one class having light-tailed properties, the other one exhibiting heavy-tailed characteristics. The heterogeneity in service requirements reflects the extreme variability in flow sizes observed in the Internet, with a vast majority of small transfers ('mice') and a limited number of exceptionally large flows ('elephants'). The active traffic flows share the available bandwidth in a Processor-Sharing (PS) fashion. The PS discipline has emerged as a natural paradigm for modeling the flow-level performance of bandwidth-sharing protocols like TCP. The number of simultaneously active traffic flows is limited by a threshold on the maximum system occupancy. We obtain the exact asymptotics of the transfer delays incurred by the users from the light-tailed class. The results show that the threshold mechanism significantly reduces the detrimental performance impact of the heavy-tailed class.
Motivated by scheduling in cellular wireless networks and resource allocation in computer systems... more Motivated by scheduling in cellular wireless networks and resource allocation in computer systems, we study a service facility with two classes of users having heterogeneous service requirement distributions. The aggregate service capacity is assumed to be largest when both classes are served in parallel, but giving preferential treatment to one of the classes may be advantageous when aiming at minimization of the number of users, or when classes have different economic values, for example. We set out to determine the allocation policies that minimize the total number of users in the system. For some particular cases we can determine the optimal policy exactly, but in general this is not analytically feasible. We then study the optimal policies in the fluid regime, which prove to be close to optimal in the original stochastic model. These policies can be characterized by either linear or exponential switching curves. We numerically compare our results with existing approximations based on optimization in the heavy-traffic regime. By simulations we show that, in general, our simple computable switching-curve strategies based on the fluid analysis perform well.
We consider an M/M/1 queue in a semi-Markovian environment. The environment is modeled by a two-s... more We consider an M/M/1 queue in a semi-Markovian environment. The environment is modeled by a two-state semi-Markov process with arbitrary sojourn time distributions F 0 ( x ) and F 1 ( x ). When in state i = 0, 1, customers are generated according to a Poisson process with intensity λ i and customers are served according to an exponential distribution with rate μ i . Using the theory of Riemann-Hilbert boundary value problems we compute the z -transform of the queue-length distribution when either F 0 ( x ) or F 1 ( x ) has a rational Laplace-Stieltjes transform and the other may be a general --- possibly heavy-tailed --- distribution. The arrival process can be used to model bursty traffic and/or traffic exhibiting long-range dependence, a situation which is commonly encountered in networking. The closed-form results lend themselves for numerical evaluation of performance measures, in particular the mean queue-length.
2010 22nd International Teletraffic Congress (lTC 22), 2010
In multi-class communication networks, traffic surges due to one class of users can significantly... more In multi-class communication networks, traffic surges due to one class of users can significantly degrade the performance for other classes. During these transient periods, it is thus of crucial importance to implement priority mechanisms allowing the conservation of the quality of service experienced by the affected classes, while ensuring that the temporarily unstable class is not entirely neglected. In this paper, we examine-for a suitably-scaled set of parameters-the complex interaction occurring between several classes of traffic when an unstable class is penalized proportionally to its level of congestion. We characterize the evolution of the performance measures of the network from the moment the initial surge takes place until the system reaches its equilibrium. We show that, using a time-space-transition-scaling, the trajectories of the temporarily unstable class can be described by a differential equation, while those of the stable classes retain their stochastic nature. In particular, we show that the temporarily unstable class evolves at a timescale which is much slower than that of the stable classes. Although the timescales decouple, the dynamics of the temporarily unstable and the stable classes continue to influence one another. We further proceed to characterize the obtained differential equations for several simple network examples. In particular, the macroscopic asymptotic behavior of the unstable class allows us to gain important qualitative insights on how the bandwidth allocation affects performance.
Modeling the interaction of IEEE 802.3x hop-by-hop flow control and TCP end-to-end flow control A... more Modeling the interaction of IEEE 802.3x hop-by-hop flow control and TCP end-to-end flow control ABSTRACT Ethernet is rapidly expanding beyond its niche of local area networks. However, its success in larger metropolitan area networks will be determined by its ability to combine simplicity, low costs and quality of service. A key element in successfully transporting bursty traffic and at the same time providing QoS, is congestion control. The Ethernet standard IEEE 802.3x defines a hop-by-hop congestion control mechanism. The performance of this scheme generally depends on its interaction with higher layer application traffic, and especially, with TCP controlled traffic which has its own end-to-end congestion control mechanism. In this paper we focus on the performance modeling and analysis of this interaction. Our model takes into account the influence of various network and traffic parameters. The validity of the proposed model is assessed by comparison of the results to simulations. In our experiments we observe that an increase of the round trip time has a positive influence on the interaction of hop-by-hop and TCP congestion control, and that the use of hop-by-hop flow control is only beneficial when the load is not high.
Web measurements have shown that TCP flow sizes vary over several orders of magnitude. If network... more Web measurements have shown that TCP flow sizes vary over several orders of magnitude. If network resources are shared fairly, the performance of short TCP flows is seriously degraded by long flows. This motivates prioritization of short over long flows, leading to significant performance improvement for short flows, with very little degradation for long ones. By imposing an appropriate pricing structure, users can be provided with incentives so as to enforce such a prioritization in a distributed manner. We study the situation where users randomly generate elastic flows (according to a Poisson process), whose sizes have a general probability distribution. Users may choose between two service classes that share the available resources with preemptive priority for one class. We assume fair sharing within each class and use a processor-sharing model with two priority classes to evaluate flow transmission times. For given price functions, users choose the service that best fits their profile, or refrain from service (`balk') if the prices exceed the willingness to pay for both services. We show that under mild modeling assumptions, the revenue maximizing Nash equilibrium is such that short flows opt for the premium service and long flows for the low-priority service. It is optimal for medium-sized flows to balk when the offered load is relatively high. Although this allocation is the result of distributed control, aside from the flows that balk, it accomplishes precisely the prioritization of short flows which improves overall performance as mentioned above.
While the (Egalitarian) Processor-Sharing (PS) discipline offers crucial insights in the performa... more While the (Egalitarian) Processor-Sharing (PS) discipline offers crucial insights in the performance of fair resource allocation mechanisms, it is inherently limited in analyzing and designing differentiated scheduling algorithms such as Weighted Fair Queueing and Weighted Round-Robin. The Discriminatory Processor-Sharing (DPS) and Generalized Processor-Sharing (GPS) disciplines have emerged as natural generalizations for modeling the performance of such service differentiation mechanisms. A further extension of the ordinary PS policy is the Multilevel Processor-Sharing (MLPS) discipline, which has captured a pivotal role in the analysis, design and implementation of size-based scheduling strategies. We review various key results for DPS, GPS and MLPS models, highlighting to what extent these disciplines inherit desirable properties from ordinary PS or are capable of delivering service differentiation.
This paper surveys the M/G/1 queue with regularly varying service requirement distribution. It st... more This paper surveys the M/G/1 queue with regularly varying service requirement distribution. It studies the effect of the service discipline on the tail behavior of the waiting-time and/or sojourn-time distribution, demonstrating that different disciplines lead to quite different tail behavior. The orientation of the paper is methodological: We outline four different methods for determining tail behavior, illustrating them for service disciplines like FCFS, Processor Sharing and LCFS.
This paper is motivated by the increasing popularity of streaming media applications that are off... more This paper is motivated by the increasing popularity of streaming media applications that are offered via the Internet. Packet streams generated by media application servers are distorted due to variability in the available bandwidth; at the receiving end, a play-out buffer compensates for the distortion. We study the dynamics of this system in a queuing-theoretical setting, using fluid analysis. To this end, we consider a model in which a constant bit-rate (CBR) media application is streamed over an unreliable network. Our model consists of a tandem of two fluid queues. The first queue is a Markov Modulated fluid queue that models the network congestion, and the second queue represents the play-out buffer. For this model the distribution of the total amount of fluid in the congestion and play-out buffers corresponds to the distribution of the maximum attained level of the first buffer. We show that the distribution of the total amount of fluid converges to a Gumbel extreme value distribution. From this result, we derive a simple closed-form expression for the initial playout-buffer level that provides a probabilistic guarantee for undisturbed playback.
Allegra, G. and Bassi, L 14/.: Isomorphism in Synthetic Macromolecular Systems. Vol. 6, pp. 549-5... more Allegra, G. and Bassi, L 14/.: Isomorphism in Synthetic Macromolecular Systems. Vol. 6, pp. 549-574. Andrews, E. H. : Molecular Fracture in Polymers. Vol. 27, pp. 1-66. Anufrieva, E. V. and Gotlib, Yu. Ya. : Investigation of Polymers in Solution by Polarized Luminescence. Vol. 40, pp. 1-68. Apicella, A., Nicolais, L. and de Cataldis, C. : Characterization of the Morphological Fine Structure of Commercial Thermosetting Resins Through Hygrothermal Experiments. Vol. 66, pp. 189-208. Argon, A. S., Cohen, R. E., Gebizlioglu, O. S. and Schwier, C. : Crazing in Block Copolymers and Blends. Vol. 52/53, pp. 275-334 Arridge, R. C. and Barham, P. J.: Polymer Elasticity. Discrete and Continuum Models. Vol. 46, pp. 67-117. Aseeva, R. M., Zaikov, G. E.: Flammability of Polymeric Materials. Vol. 70, pp. 171-230. Ayrey, G.: The Use of Isotopes in Polymer Analysis. Vol. 6, pp. 128-148.
Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications, 2006
We show that different flavors of TCP may be viewed as implementations of age-based scheduling di... more We show that different flavors of TCP may be viewed as implementations of age-based scheduling disciplines. By parameterizing the scheduling disciplines of interest we are able to position variants of TCP in a wide spectrum having FCFS (First-Come First-Served) and LAS (Least Attained Service first) as extremal policies, and including PS (Processor Sharing) as an intermediate case. We argue that for highly loaded systems, providing a fair bandwidth allocation among all users is secondary to ensuring network stability. So as to isolate protocol fairness from congestion effects, we therefore focus on scenarios with infinite buffers. This way, asymmetries in capacity shares are the consequences of the protocol only, and not affected by the packet loss process. The model, however, is flexible enough to include finite buffers with random packet loss as a special case (for example to capture Active Queue Management). The results are helpful in studying fairness and performance concerned with transmission protocols in communication networks. For persistent HTTP connections we study the distributions of the transmission rates and the relative fairness index under various assumptions on the file size distributions and scheduling disciplines. For infinite file sizes, we show that protocols that increase priority more than linearly with the attained service asymptotically behave similar to FCFS. In contrast, protocols with at most linearly increasing (or even decreasing) priority, with TCP's Congestion Avoidance mechanism as the most prominent example, converge to PS scheduling (even in absence of losses). When the priority is exactly linear in the attained service, such as for Scalable TCP and TCP's Slow Start phase, the shares remain constant in between file initiations and completions. 1 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the Proceedings IEEE Infocom.
We consider a system with two heterogeneous traffic classes. The users from both classes randomly... more We consider a system with two heterogeneous traffic classes. The users from both classes randomly generate service requests, one class having light-tailed properties, the other one exhibiting heavy-tailed characteristics. The heterogeneity in service requirements reflects the extreme variability in flow sizes observed in the Internet, with a vast majority of small transfers ('mice') and a limited number of exceptionally large flows ('elephants'). The active traffic flows share the available bandwidth in a Processor-Sharing (PS) fashion. The PS discipline has emerged as a natural paradigm for modeling the flow-level performance of bandwidth-sharing protocols like TCP. The number of simultaneously active traffic flows is limited by a threshold on the maximum system occupancy. We obtain the exact asymptotics of the transfer delays incurred by the users from the light-tailed class. The results show that the threshold mechanism significantly reduces the detrimental performance impact of the heavy-tailed class.
Motivated by scheduling in cellular wireless networks and resource allocation in computer systems... more Motivated by scheduling in cellular wireless networks and resource allocation in computer systems, we study a service facility with two classes of users having heterogeneous service requirement distributions. The aggregate service capacity is assumed to be largest when both classes are served in parallel, but giving preferential treatment to one of the classes may be advantageous when aiming at minimization of the number of users, or when classes have different economic values, for example. We set out to determine the allocation policies that minimize the total number of users in the system. For some particular cases we can determine the optimal policy exactly, but in general this is not analytically feasible. We then study the optimal policies in the fluid regime, which prove to be close to optimal in the original stochastic model. These policies can be characterized by either linear or exponential switching curves. We numerically compare our results with existing approximations based on optimization in the heavy-traffic regime. By simulations we show that, in general, our simple computable switching-curve strategies based on the fluid analysis perform well.
We consider an M/M/1 queue in a semi-Markovian environment. The environment is modeled by a two-s... more We consider an M/M/1 queue in a semi-Markovian environment. The environment is modeled by a two-state semi-Markov process with arbitrary sojourn time distributions F 0 ( x ) and F 1 ( x ). When in state i = 0, 1, customers are generated according to a Poisson process with intensity λ i and customers are served according to an exponential distribution with rate μ i . Using the theory of Riemann-Hilbert boundary value problems we compute the z -transform of the queue-length distribution when either F 0 ( x ) or F 1 ( x ) has a rational Laplace-Stieltjes transform and the other may be a general --- possibly heavy-tailed --- distribution. The arrival process can be used to model bursty traffic and/or traffic exhibiting long-range dependence, a situation which is commonly encountered in networking. The closed-form results lend themselves for numerical evaluation of performance measures, in particular the mean queue-length.
2010 22nd International Teletraffic Congress (lTC 22), 2010
In multi-class communication networks, traffic surges due to one class of users can significantly... more In multi-class communication networks, traffic surges due to one class of users can significantly degrade the performance for other classes. During these transient periods, it is thus of crucial importance to implement priority mechanisms allowing the conservation of the quality of service experienced by the affected classes, while ensuring that the temporarily unstable class is not entirely neglected. In this paper, we examine-for a suitably-scaled set of parameters-the complex interaction occurring between several classes of traffic when an unstable class is penalized proportionally to its level of congestion. We characterize the evolution of the performance measures of the network from the moment the initial surge takes place until the system reaches its equilibrium. We show that, using a time-space-transition-scaling, the trajectories of the temporarily unstable class can be described by a differential equation, while those of the stable classes retain their stochastic nature. In particular, we show that the temporarily unstable class evolves at a timescale which is much slower than that of the stable classes. Although the timescales decouple, the dynamics of the temporarily unstable and the stable classes continue to influence one another. We further proceed to characterize the obtained differential equations for several simple network examples. In particular, the macroscopic asymptotic behavior of the unstable class allows us to gain important qualitative insights on how the bandwidth allocation affects performance.
Modeling the interaction of IEEE 802.3x hop-by-hop flow control and TCP end-to-end flow control A... more Modeling the interaction of IEEE 802.3x hop-by-hop flow control and TCP end-to-end flow control ABSTRACT Ethernet is rapidly expanding beyond its niche of local area networks. However, its success in larger metropolitan area networks will be determined by its ability to combine simplicity, low costs and quality of service. A key element in successfully transporting bursty traffic and at the same time providing QoS, is congestion control. The Ethernet standard IEEE 802.3x defines a hop-by-hop congestion control mechanism. The performance of this scheme generally depends on its interaction with higher layer application traffic, and especially, with TCP controlled traffic which has its own end-to-end congestion control mechanism. In this paper we focus on the performance modeling and analysis of this interaction. Our model takes into account the influence of various network and traffic parameters. The validity of the proposed model is assessed by comparison of the results to simulations. In our experiments we observe that an increase of the round trip time has a positive influence on the interaction of hop-by-hop and TCP congestion control, and that the use of hop-by-hop flow control is only beneficial when the load is not high.
Web measurements have shown that TCP flow sizes vary over several orders of magnitude. If network... more Web measurements have shown that TCP flow sizes vary over several orders of magnitude. If network resources are shared fairly, the performance of short TCP flows is seriously degraded by long flows. This motivates prioritization of short over long flows, leading to significant performance improvement for short flows, with very little degradation for long ones. By imposing an appropriate pricing structure, users can be provided with incentives so as to enforce such a prioritization in a distributed manner. We study the situation where users randomly generate elastic flows (according to a Poisson process), whose sizes have a general probability distribution. Users may choose between two service classes that share the available resources with preemptive priority for one class. We assume fair sharing within each class and use a processor-sharing model with two priority classes to evaluate flow transmission times. For given price functions, users choose the service that best fits their profile, or refrain from service (`balk') if the prices exceed the willingness to pay for both services. We show that under mild modeling assumptions, the revenue maximizing Nash equilibrium is such that short flows opt for the premium service and long flows for the low-priority service. It is optimal for medium-sized flows to balk when the offered load is relatively high. Although this allocation is the result of distributed control, aside from the flows that balk, it accomplishes precisely the prioritization of short flows which improves overall performance as mentioned above.
While the (Egalitarian) Processor-Sharing (PS) discipline offers crucial insights in the performa... more While the (Egalitarian) Processor-Sharing (PS) discipline offers crucial insights in the performance of fair resource allocation mechanisms, it is inherently limited in analyzing and designing differentiated scheduling algorithms such as Weighted Fair Queueing and Weighted Round-Robin. The Discriminatory Processor-Sharing (DPS) and Generalized Processor-Sharing (GPS) disciplines have emerged as natural generalizations for modeling the performance of such service differentiation mechanisms. A further extension of the ordinary PS policy is the Multilevel Processor-Sharing (MLPS) discipline, which has captured a pivotal role in the analysis, design and implementation of size-based scheduling strategies. We review various key results for DPS, GPS and MLPS models, highlighting to what extent these disciplines inherit desirable properties from ordinary PS or are capable of delivering service differentiation.
This paper surveys the M/G/1 queue with regularly varying service requirement distribution. It st... more This paper surveys the M/G/1 queue with regularly varying service requirement distribution. It studies the effect of the service discipline on the tail behavior of the waiting-time and/or sojourn-time distribution, demonstrating that different disciplines lead to quite different tail behavior. The orientation of the paper is methodological: We outline four different methods for determining tail behavior, illustrating them for service disciplines like FCFS, Processor Sharing and LCFS.
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