A Characterization of Universal Stability in the Adversarial Queuing Model

Àlvarez, Carme; Blesa, Miguel A.; Serna, María

doi:10.1137/s0097539703435522

Cited by 40 publications

(37 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They showed the existence of an acknowledgment based protocol that has fair latency for injection rates at most 1 cn lg 2 n , for some c > 0, and developed an explicit acknowledgment based protocol that has fair latency for injection rates at most 1 27n 2 ln n . Finally, they showed that no acknowledgement-based protocol is stable for injection rates larger than 3 1+lg n . Algorithmic problems not regarding pure communication issues in distributed environments relying on multiple access channels have been also studied in the literature.…”

Section: Related Workmentioning

confidence: 99%

Maximum throughput of multiple access channels in adversarial environments

2009

View full text Add to dashboard Cite

We consider deterministic distributed broadcasting on multiple access channels in the framework of adversarial queuing. Packets are injected dynamically by an adversary that is constrained by the injection rate and the number of packets that may be injected simultaneously; the latter we call burstiness. A protocol is stable when the number of packets in queues at the stations stays bounded. The maximum injection rate that a protocol can handle in a stable manner is called the throughput of the protocol. We consider adversaries of injection rate 1, that is, of one packet per round, to address the question if the maximum throughput 1 can be achieved, and if so then with what quality of service. We develop a protocol that achieves throughput 1 for any number of stations against leaky-bucket adversaries.The results of this paper appeared in a preliminary form in 'Stability of multiple access channels under maximum broadcast loads' in The protocol has O(n 2 + burstiness) packets queued simultaneously at any time, where n is the number of stations; this upper bound is proved to be best possible. A protocol is called fair when each packet is eventually broadcast. We show that no protocol can be both stable and fair for a system of at least two stations against leaky-bucket adversaries. We study in detail small systems of exactly two and three stations against window adversaries to exhibit differences in quality of broadcast among classes of protocols. A protocol is said to have fair latency if the waiting time of packets is O(burstiness). For two stations, we show that fair latency can be achieved by a full sensing protocol, while there is no stable acknowledgment based protocol. For three stations, we show that fair latency can be achieved by a general protocol, while no full sensing protocol can be stable. Finally, we show that protocols that either are fair or do not have the queue sizes affect the order of transmissions cannot be stable in systems of at least four stations against window adversaries.

show abstract

Section: Related Workmentioning

confidence: 99%

Maximum throughput of multiple access channels in adversarial environments

2009

View full text Add to dashboard Cite

show abstract

“…The subfield of proposing a characterization for universally stable networks was first initiated in [3,6] proving that certain well-known network topologies (DAGs, trees, ring) are universally stable. These results were significantly improved by Gamarnik [10] presenting a tight characterization of stable topologies for undirected graphs and by Goel [11] and Alvarez et al [2] proving a tight characterization of stable topologies for directed graphs.…”

Section: Related Workmentioning

confidence: 94%

“…They proved that many 2 NTS gives priority to the nearest packet to its origin in the network. 3 FTG gives priority to the furthest packet from its destination in the network.…”

Section: Related Workmentioning

confidence: 99%

Performance and stability bounds for dynamic networks

Koukopoulos

Mavronicolas

Spirakis

2007

Journal of Parallel and Distributed Computing

View full text Add to dashboard Cite

In this work, we study the impact of dynamically changing link capacities on the delay bounds of LIS (Longest-In-System) and SIS (Shortest-In-System) protocols on specific networks (that can be modelled as Directed Acyclic Graphs (DAGs)) and stability bounds of greedy contention-resolution protocols running on arbitrary networks under the Adversarial Queueing Theory. Especially, we consider the model of dynamic capacities, where each link capacity may take on integer values from [1, C] with C > 1, under a (w, )-adversary. We show that the packet delay on DAGs for LIS is upper bounded by O(iw C) and lower bounded by (iw C) where i is the level of a node in a DAG (the length of the longest path leading to node v when nodes are ordered by the topological order induced by the graph). In a similar way, we show that the performance of SIS on DAGs is lower bounded by (iw C), while the existence of a polynomial upper bound for packet delay on DAGs when SIS is used for contention-resolution remains an open problem. We prove that every queueing network running a greedy contention-resolution protocol is stable for a rate not exceeding a particular stability threshold, depending on C and the length of the longest path in the network.

show abstract

“…Thus, those results concerning universal stability can be transferred from one model to the other. Therefore, according to the results in [1] and [2], we can state the following, Corollary 1 Directed acyclic graphs and rings are universally stable in the ½ model. …”

Section: The ½ Modelmentioning

confidence: 85%

“…On the contrary, the main goal of the model is to study conditions for stability of the network under different protocols. A considerable amount of results is available nowadays (see, e.g., [9,3,11,2,17,14,18,1,8,12,16,2]). …”

Section: Introductionmentioning

confidence: 99%

The impact of failure management on the stability of communication networks

Àlvarez¹,

Blesa²,

Serna³

Proceedings. Tenth International Conference on Parallel and Distributed Systems, 2004. ICPADS 2004.

View full text Add to dashboard Cite

In this work we deal with communication networks in which links may fail. We propose an adversarial model for describing the traffic pattern occurring in this type of faulty systems and study properties concerning their stability, specially under (non-trivial) underloaded worse-case scenarios. We show that, depending on how the system is organized and prepared to deal with failures, the dynamics of the system change and thus the conditions for stability. We propose three different ways of failure management and study how they influence on the stability of faulty communication networks under the adversarial model proposed. We show that some failure managements can provoke the instability of even very simple networks.

show abstract

A Characterization of Universal Stability in the Adversarial Queuing Model

Cited by 40 publications

References 20 publications

Maximum throughput of multiple access channels in adversarial environments

Maximum throughput of multiple access channels in adversarial environments

Performance and stability bounds for dynamic networks

The impact of failure management on the stability of communication networks

Contact Info

Product

Resources

About