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## Scheduling Nonuniform Traffic In A Packet Switching System With Small Propagation Delay (1994)

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Venue: | IEEE/ACM Transactions on Networking |

Citations: | 69 - 2 self |

### Citations

2209 | Data Networks - Bertsekas, Gallager - 1992 |

667 |
A calculus for network delay, Part I; network elements in isolation,”
- Cruz
- 1991
(Show Context)
Citation Context ...1 1 A 1 k+1 k+2 k Figure 2: Matrix sequences assumed that the switching time is zero. 1.3 A New Non-Uniform Traffic Model Many models of nonuniform traffic streams have been proposed (see for example =-=[9, 10, 11]-=-). These can generally be classified into two categories. Random models have random arrivals with a specified distribution that allows for the possibility of nonuniform traffic matrix sequences. Examp... |

527 | Achieving 100% Throughput in an Input-Queued Switch,”
- Mckeown, Mekkittikul, et al.
- 1999
(Show Context)
Citation Context ...that is independent and identically distributed in time and possibly asymmetrical with respect to destination nodes. Also, interesting stability results have been proved in [7, see Proposition 3] and =-=[8]-=- for random traffic and scheduling algorithms based on weighted maximum matchings. 1.2 Notation and assumptions Let N = f1; : : : ng index the set of stations. The virtual queues of source i are label... |

338 |
Input versus output queueing on a space division switch,”
- Karol, Hluchyj, et al.
- 1984
(Show Context)
Citation Context ...rce queues are more accessible. The classic result for uniform random traffic is that HOL blocking at the source queues limits the maximum throughput to about 0.58 for any transmission algorithm (see =-=[20]-=- for example). For nonuniform traffic patterns, the HOL blocking problem can be much worse. To illustrate that the HOL blocking problem with (ff; S) traffic can be severe, a simpler, related problem i... |

296 |
Universal schemes for parallel communication”,
- Valiant, Brebner
- 1981
(Show Context)
Citation Context ...most ffS packets, where S is a positive integer, and 0 ! ffs1. For convenience, ffS is taken to be an integer. This traffic model is a "continuousarrival " variant of the notion of partial h=-=-relation [12]-=-, in which there is a batch of packets to route, at most h starting at any node and at most h destined for any node. The parameter ff represents the maximum long-run throughput allowed for any source ... |

254 |
Combinatorial Theory,
- Hall
- 1967
(Show Context)
Citation Context ...ic matrix. Several scheduling algorithms for (ff; S) traffic are derived here from the principles behind the solution of the TSA problem for SS/TDMA. A fundamental result of combinatorial mathematics =-=[15]-=- is that any traffic matrix with maximum line sum m can be represented as the sum of m switching matrices. Any algorithm which finds such an assignment is said to be 100% efficient. It is well known t... |

154 |
On Computing Per-Session Performance Bounds in High-Speed Multi-Hop Computer Networks.
- Kurose
- 1992
(Show Context)
Citation Context ...1 1 A 1 k+1 k+2 k Figure 2: Matrix sequences assumed that the switching time is zero. 1.3 A New Non-Uniform Traffic Model Many models of nonuniform traffic streams have been proposed (see for example =-=[9, 10, 11]-=-). These can generally be classified into two categories. Random models have random arrivals with a specified distribution that allows for the possibility of nonuniform traffic matrix sequences. Examp... |

139 |
Introduction to Combinatorial Mathematics.
- Liu
- 1968
(Show Context)
Citation Context ...inite. For a continuous scheduling algorithm using maximum matchings, For a continuous scheduling algorithm using maximal matchings, Proof: In the notation of this paper, the König–Egerváry theorem =-=[23]-=- states that the cardinality of a maximum matching on a backlog graph is equal to the minimum number of lines in the associated backlog matrix which together contain all of the nonzero entries. Let an... |

130 |
A new architecture for packet switching network protocols,”
- Zhang
- 1989
(Show Context)
Citation Context ...owing away excess packets, perhaps chosen by matchings, probably yields a near-minimum number of dropped packets. With current knowledge, the (ff; S) traffic model is best used in a system such as in =-=[22]-=- where virtual circuits (between a source-destination pair) reserve bandwidth in advance, respecting the (ff; S) constraint. Such connection-oriented traffic is most easily supported, but datagram tra... |

91 |
Scheduling and performance limits of networks with constatly varying topology,
- Tassiulas
- 1997
(Show Context)
Citation Context ...ansmissions in each slot as a function of only which source-destination pairs have at least one packet waiting. Perhaps a method based on maximum weighted matchings, as proposed for random traffic in =-=[7, 8]-=-, would be fruitful. Given the fact that BATCH MAXIMUM algorithms can achieve ff = 1 with good performance bounds, it may not warrant much additional effort, unless a very simple algorithm is found. F... |

83 |
Multi-Wavelength Lightwave Networks for Computer Communication
- Ramaswami
- 1993
(Show Context)
Citation Context ...methods for transmitting nonuniform traffic in a simple packet switching system. A new model of nonuniform traffic is introduced which is based on traffic constraints. Most previous related work (see =-=[1]-=- for an overview) has focused on uniform traffic patterns. Traditional approaches such as time-division multiplexing and pure random contention schemes are not well-suited for nonuniform traffic. At l... |

69 |
A media access protocol for packet-switched wave length division multiaccess metropolitan area networks
- Chen, Dono, et al.
- 1990
(Show Context)
Citation Context ...et switching system considered in this paper has many stations with a fully connected topology (see Figure 1). This multiple-access communication model was used previously to analyze optical networks =-=[2, 3]-=-, but its application can be broader. Each station is both a source and destination 1 and each has a data transmitter and receiver. The fully connected topology is realized by dedicating a data channe... |

53 |
An efficient SS/TDMA time slot assignment algorithm
- Inukai
- 1979
(Show Context)
Citation Context ...als the traffic matrix. The duration of the assignment is the length of the sequence. The number of modes of the assignment is the number of unique switching matrices in the sequence. The TSA problem =-=[13]-=- can be stated simply: Given a traffic matrix, find an assignment of minimum duration which also minimizes the number of switching modes. This problem has been shown to be NP-complete [14]. For small ... |

50 |
Algorithms for edge coloring bipartite graphs and multigraphs
- Gabow, Kariv
- 1982
(Show Context)
Citation Context ...e done in time O(n 2 ). Note that a maximum matching is a maximal matching. See [16] for details. assignment of at least four slots.) Fast algorithms presented for edge coloring bipartite graphs (see =-=[17]-=- for example) can also be used on the TSA problem. The critical maximum matching method for the TSA solution is better suited for continuous operation, as dicussed in Section 3. 1 1 1 1 1 1 1 2 1 + + ... |

43 |
Minimizing the Number of Switchings in an SS/TDMA System
- Gopal, Wong
- 1985
(Show Context)
Citation Context ...TSA problem [13] can be stated simply: Given a traffic matrix, find an assignment of minimum duration which also minimizes the number of switching modes. This problem has been shown to be NP-complete =-=[14]-=-. For small (or zero) switching times, the goal is simply to find a minimum duration assignment. In the packet switching context, it is also desirable to find assignments which minimize the delay of p... |

27 |
A growable packet ~ATM! switch architecture: design principles and applications,’’
- Eng, Karol, et al.
- 1992
(Show Context)
Citation Context ...ntly large, some algorithms in BATCH MAXIMUM (and hence some algorithms in BATCH MAXIMAL ) do not have any of the properties P1--P3. The distributed routing algorithm for a packet switch described in =-=[18]-=- provides the inspiration for a class of algorithms introduced here called PARALLEL MAXIMAL, which is similar to the class BATCH MAXIMAL. For a given batch, consider an empty scheduling grid with n ro... |

25 |
A wavelength division multiple access network for computer communication”,
- Dono, Jr, et al.
- 1990
(Show Context)
Citation Context ...et switching system considered in this paper has many stations with a fully connected topology (see Figure 1). This multiple-access communication model was used previously to analyze optical networks =-=[2, 3]-=-, but its application can be broader. Each station is both a source and destination 1 and each has a data transmitter and receiver. The fully connected topology is realized by dedicating a data channe... |

22 |
An Optimum Time Slot Assignment Algorithm for an SS/TDMA System with Variable Number of Transponders
- Bongiovanni, Coppersmith, et al.
- 1981
(Show Context)
Citation Context ... is wasteful for some values of c such as c = 1:2. By allowing any n c sources to transmit in any slot, this waste can be eliminated. Using a BATCH TSA algorithm with a time slot assignment scheme in =-=[19]-=-, each batch with maximum line sum ffS can be scheduled in dcffSe slots, which is optimal. The PARALLEL MAXIMAL algorithms, described in Section 2, are also easily modified for use with a reduced numb... |

8 |
Stochastic Models for ATM Switching Networks
- Descloux
- 1991
(Show Context)
Citation Context ...1 1 A 1 k+1 k+2 k Figure 2: Matrix sequences assumed that the switching time is zero. 1.3 A New Non-Uniform Traffic Model Many models of nonuniform traffic streams have been proposed (see for example =-=[9, 10, 11]-=-). These can generally be classified into two categories. Random models have random arrivals with a specified distribution that allows for the possibility of nonuniform traffic matrix sequences. Examp... |

3 |
Chang et al., “Implementation of STARNET: A WDM computer communications network
- K
- 1996
(Show Context)
Citation Context ... station needs a fixed transmitter and a fixed receiver on this wavelength. RAINBOW is designed primarily for use in metropolitan-area networks. A similar broadcast and select network is described in =-=[4]-=-. The basic model can also be applied to large all-electronic switches with input buffering. Each source has a buffer to hold the queue of packets which have not yet been sent. More than one packet ca... |

1 |
Implementation of STARNET: a WDM computer communications network
- al
- 1996
(Show Context)
Citation Context ... station needs a fixed transmitter and a fixed receiver on this wavelength. RAINBOW is designed primarily for use in metropolitan area networks. A similar broadcast and select network is described in =-=[4]-=-. The basic model can also be applied to large all-electronic switches with input buffering. Each source has a buffer to hold the queue of packets which have not yet been sent. More than one packet ca... |

1 |
A conflict free protocol for optical WDMA networks
- Chen, Yum
- 1991
(Show Context)
Citation Context ...e analysis of scheduling algorithms given in this paper is based on deterministically constrained traffic, similar algorithms have been shown to have good performance for random traffic. For example, =-=[6]-=- considers an algorithm in the class CONTINUOUS STATIC defined in this paper, and shows good performance for traffic that is independent and identically distributed in time and possibly asymmetrical w... |