D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... is inversely proportional to # p, which is the packet loss probability in the network [16] Also, it is known that, if the bottleneck router in the network can be modeled by a single M M 1 queueing system, the average queue length is given by # (1 #) where # is the utilization factor [17]. Hence, on the basis of the fact that the primary purpose of AQM mechanisms is to control the average queue length, it is considered that the packet marking probability of RED should not be changed linearly in relation to the average queue length. Of course, rather than using a simple queuing ....

D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

.... a recently proposed switch algorithm called as the max min scheme [8] A strong point of this algorithm compared with others is that it can satisfy max min fairness for any network configuration; that is, total throughput of the network is maximized and fairness among connections is maintained [9]. However, its defect is in lack of adaptability to changes in the network (e.g. connection addition disconnection) as will be demonstrated in Section 3. Thus, we propose our enhancements to the max min scheme to improve its stability and efficiency. We also evaluate its performance by comparing ....

D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

....a Markov process. Accordingly, the state vector n forms a multi dimensional Markov chain. This type of chain is usually difficult to analyze than the one dimensional Markov chain, but in many interesting special cases we can obtain a closed form solution for the stationary distribution p( n) [2]. If we deal with this problem using Jackson network [2] as shown in Fig. 2, we can find a closed form solution. First, we assume that there are K queues (or spotbeams) and each queueing system has m i servers, where i 2 fA, B, C, D, E, F , Gg. In our case, K = 7. Second, we assume the external ....

....forms a multi dimensional Markov chain. This type of chain is usually difficult to analyze than the one dimensional Markov chain, but in many interesting special cases we can obtain a closed form solution for the stationary distribution p( n) 2] If we deal with this problem using Jackson network [2], as shown in Fig. 2, we can find a closed form solution. First, we assume that there are K queues (or spotbeams) and each queueing system has m i servers, where i 2 fA, B, C, D, E, F , Gg. In our case, K = 7. Second, we assume the external arrival process to the i th queue is Poisson with rate ....

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D. Bertsekas and R. Gallager, Data Networks, 2nd ed. New Jersey: Prentice-Hall, 1992.

....burst errors are the chief cause of faults in the header [15] In order to simplify the analysis, only burst errors are taken into account. Consider a CRC of length Z to check the integrity of a data block of length K. Then Z should be chosen such that it satis es the following inequality [2]: 2 Z 1 Z K 1: 8) Such a CRC is guaranteed to correct all single errors and detect double errors (SEC DED code) and it fails to detect burst errors with probability (K Z 1)2 Z : WINE 453.tex; 23 08 2001; 19:13; p.9 10 Hocan n, Sarin and Deli c CRC frame Frame n Frame 1 Input ....

D. Bertsekas and R. B. Gallager, Data Networks, Englewood Clis, New Jersey: Prentice-Hall, 1987.

.... a recently proposed switch algorithm called as the max min scheme [7] A strong point of this algorithm compared with others is that it can satisfy max min fairness for any network configuration; that is, total throughput of the network is maximized while fairness among connections is maintained [8]. However, its defect is in lack of adaptability to changes in the network (e.g. connection addition disconnection) as will be demonstrated in Section III. Thus, we propose our enhancements to the max min scheme to improve its stability and efficiency. We also evaluate its performance through ....

D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

....be regarded as the minimum guaranteed throughput for the bursty traffic. Since the stream traffic is given high priority, it can be modeled by an M M m m queuing system. By letting n be the probability that n calls of stream traffic are accepted in steady state, n is given as follows (e.g. [12]) n = m X n=0 CBR CBR n 1 n # Gamma1 CBR CBR n 1 n Since the service time of steam traffic can be assumed to be much longer than cell or the packet transmission time of bursty traffic, the available link capacity for bursty traffic is regarded to be constant when the ....

D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

....is no definition of the fairness measure in the literature, the ATM forum is also discussing fairness criteria. The fairness for the ABR service is defined by a max min criterion in [27] In the max min criterion, all active connections are served fairly if the following two conditions are met [28]: 1) each connection must pass through at least one bottlenecked switch, and (2) the available bandwidth should be shared fairly when it is assigned to connections that do not pass through nonbottlenecked switch. However, the max min criterion becomes inadequate for ABR traffic where MCR, the ....

D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

....below should be regarded as the minimum guaranteed throughput for the bursty traffic. Since the stream traffic is given a high priority, it can be modeled by a M M m m queueing system. By letting n be the probability that n calls of stream traffic are accepted in steady state, we have (e.g. [7]) n = m X n=0 CBR CBR n 1 n # Gamma1 CBR CBR n 1 n (38) Since the service time of steam traffic can be assumed to be much longer than cell or the packet transmission time of bursty traffic, an available link capacity to bursty traffic is regarded to be constant ....

D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

.... of the significance of the stab ility analysis in this paper and the wide numb er of applications where load b lancing pro b ems are encountered, the reader is referred to [5] The loadb alancing systems that we examine are similar to and generalizations of those analyzed in [2, 3] and in [6]. In [2, 3] the load b lancing system is very simpleb ecause the load is considered to exist only in b locks of unit size, the allowed inter processor load exchanges are quite restricted, and any delays that exist in passing load and sensing load levels are ignored. The model in [6] assumes that ....

....[2, 3] and in [6] In [2, 3] the load b lancing system is very simpleb ecause the load is considered to exist only in b locks of unit size, the allowed inter processor load exchanges are quite restricted, and any delays that exist in passing load and sensing load levels are ignored. The model in [6] assumes that load canb e representedb y a continuous variab le and that delays exist in load passing and sensing. The model also allows for general load passing. The authors in [6] show that eventually the load willb e perfectly b lanced among the processors, and they suggest a proof for the ....

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J. Tsitsiklis and D. Bertsekas, Parallel and Distrib uted Computation. New Jersey: Prentice-Hall, Inc., 1989.

....and waste of the queue capacity due to underflow. Fairness is an issue which deserves a little more discussion, as it may be hard to visualize what is meant by a fair allocation in a large network with multiple bottlenecks. A widely accepted notion of fairness is the max min fairness criterion [10]. Under this criterion the fair share of each connection contending for a given link bandwidth at the output port of a particular switch should be equal to # ######## # #### # # # ### # # (2) As indicated earlier, the decision on the rate at which each controlled source should transmit is ....

D. P. Bertsekas and R. Gallager, Data Networks.NewJersey: Prentice Hall, Englewood Cliffs, 1987.

....is no definition of the fairness measure in the literature, the ATM forum is also discussing fairness criteria. The fairness for the ABR service is defined by a max min criterion in [27] In the max min criterion, all active connections are served fairly if the following two conditions are met [28]: 1) each connection must pass through at least one bottlenecked switch, and (2) the available bandwidth should be shared fairly when it is assigned to connections that do not pass through nonbottlenecked switch. However, the max min criterion becomes inadequate for ABR traffic where MCR, the ....

D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

....high low priority delays. For each station, at the end of a busy period, the slot becomes unavailable for a random period of time, rather than going back into service immediately (for the same station) Hence, the nonpreemptive slotted ring network can be modeled as an M D N queue with vacations [1]. The expected waiting time equations can be derived directly for NRAP [5] But the delay analysis of NRAP is considerably more difficult because the processing decisions depend on the waiting times. Bounds on the expected delays can be derived using the regenerative theorem [6] but conditional ....

D. Bertsekas and R. Gallager (1987): Data Networks, Englewood Cliffs, New Jersey: PrenticeHall.

....Ministry of Communications, Israel. 1 INTRODUCTION Consider a growing tree of which each vertex generates additional vertices according to some probabilistic reproduction law. Growing trees arise naturally in many applications, such as searching and sorting [8] multiaccess communication [2], and growth of populations [3] 4] Often, the tree that arises is growing in presence of a stochastic process, the random environment, which determines the reproduction law of each vertex. In addition, the tree may consist of vertices of different types, and the reproduction law of each vertex ....

....is referred to as Depth First Order (DFO) and is defined by the following rules: 1) A parent always precedes its offsprings. 2) The vertices of a right subtree always precede the sibling of the root of this subtree (which is a left offspring) The DFO is used in existing splitting algorithms [2]. The second order is referred to as Breadth First Order (BFO) and is defined by the following rules: 1) A right offspring always (a) Under the DFO (b) Under the BFO Figure 1: Examples of binary trees growing in the environment X( fbbbgggg : g (shaded vertex type 1, unshaded vertex ....

D. Bertsekas and R. Gallager, Data Networks, New Jersey: Prentice-Hall, 1987.

....are considered here. Taking a typical burst period of 30 msec [4] and data transmission rate of 1.25 Mbps, 85 cells will be affected in this burst. Consider a CRC of length Z to check the integrity of a data block of length K. Z should be chosen such that it satisfies the following inequality [1]: 2 Z Gamma1 Gamma Z K 1: 5) Such a CRC is guaranteed to correct all single errors and detect double errors (SEC DED code) CRC fails to detect burst errors with probability (K Z 1)2 GammaZ . 1 error 1 error 0 errors Detect Only Correct (drop cell) 0 errors ( correct if 1; drop ....

D. Bertsekas and R. Gallager: Data Networks, Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

....are considered here. Taking a typical burst period of 30 msec [10] and data transmission rate of 1.25 Mbps, 85 cells will be affected in this burst. Consider a CRC of length Z to check the integrity of a data block of length K. Z should be chosen such that it satisfies the following inequality [2]: 2 Z Gamma1 Gamma Z K 1: 5) Such a CRC is guaranteed to correct all single errors and detect double errors (SEC DED code) CRC fails to detect burst errors with probability (K Z 1)2 GammaZ . 1 error 1 error 0 errors Detect Only Correct (drop cell) 0 errors ( correct if 1; drop if ....

D. Bertsekas and R. G. Gallager: Data Networks, Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

.... at the end of a busy period, the slot becomes unavailable for a random period of time, rather than going back into service immediately (for the same station) Hence, the systems that consist of the slotted ring network with nonpreemptive RAPs can be modeled as an M D 1 queue with vacations [1]. The expected waiting time equations can be derived directly for RAP1 [6] But the delay analysis of RAP2 is considerably more difficult because the processing decisions depend the on waiting times. Bounds on the expected delays can be derived using the regenerative theorem [8] but conditional ....

D. Bertsekas and R. G. Gallager (1987): Data Networks, Englewood Cliffs, New Jersey: Prentice-Hall.

....channel after shaping is regarded as the peak bandwidth of the channel, for purposes of admission control. 2.3 Routing Methods The routing problem has been investigated extensively for both circuit switched and packetswitched networks. Some recent summaries of routing techniques are by Bertsekas [5], Girard [22] and Perlman [47] The goals for routing include maximizing the load accepted by the network while providing satisfactory QoS to channels and treating all call requests equally (i.e. being fair) These goals can be contradictory, so the search for optimal algorithms is in fact quite ....

....The C DYN algorithm is a dynamic shortest path router. The length of each link is set to be inversely proportional to the spare capacity fraction (i.e. 1 utilization) of that link. This formulation corresponds to a link length equal to the average queuing delay in a network of M=M=1 queues [5]) A desirable by product is that the load on the network tends to get evenly distributed. 2.3.2 An Algorithm Based on Circuit switched Network Routing Hwang et al. [28] proposed the use of sequential routing algorithms, similar to those used in circuit switched networks such as telephone ....

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D. Bertsekas and R. Gallager, Data Networks, Englewood Cliffs, New Jersey: PrenticeHall, 2nd Ed 1992.

....the request packet, he she obtains a fraction of the channel, where the packets are delivered expeditiously. Transmission of the request packet can be either in a deterministic way such as time division multiple access (TDMA) or during a probabilistic process as in reservation Aloha (R Aloha) [2]. For low rate bursty data traffic however, reservation schemes waste capacity since during a significant portion of time, reserved resources remain unutilized. Transmission of data traffic, on the other hand, can tolerate longer delays, but it is very sensitive to channel errors and packet ....

D. Bertsekas and R. Gallager, Data Networks, 2nd Edition, Upper Saddle River, New Jersey: Prentice-Hall, 1992.

....which can be accessed by only one user at a time for successful transmission. It is assumed that there exists some form of feedback to the users regarding the status of their transmissions. The model that has consistently been adopted by researchers consists of the following idealized conditions [1]: 1. The transmission channel is slotted and noiseless. The users transmit in packets whose constant duration is one slot. A collision between two or more packets is always detected as such, but the information contained in the colliding packets is lost, making retransmissions necessary. 2. The ....

D. Bertsekas and R. G. Gallager, Data Networks, Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

....reception, decoding and display for the duration of the conference. Once the end systems have agreed upon the desired 10 service needed from the network, a suitable route through the network must be found. Many techniques for routing in packet switched networks have been proposed and used; see [19] for a survey. These techniques generally optimize either the path length (i.e. minimum number of hops) or the link utilization (i.e. minimize the maximum utilization) For real time packet networks, the need to reserve resource (whether for exclusive use by a session or in a ....

D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 2 ed., 1992.

....a cell may be stored in the buffer longer when the appropriate output channel is not available. The resulting delay is added to the cumulative delay of the cell and, when the latter exceeds a prescribed limit defined for a specific traffic class, the cell may be dropped. Bertsekas and Gallager [32] present buffer management schemes where separate buffer space is reserved for different traffic classes while some buffer space is shared by all classes. A typical choice is to assign a level of priority to a cell equal to the number of links it has traversed in the network. Spragins, Hammond, ....

....delays. In this spirit, the notion of cell blocking combines potentially useful elements of both admission control and smoothing functions. It may be observed that selective cell blocking impacts the traditional view of virtual circuits. In particular, ATM networks, standardized for broadband ISDN [32], utilize a virtual circuit connectionoriented switched architecture. This paper proposes to expand the scope of the standard ATM architecture to include a selective cell blocking option. Evidently, this feature implies some level of message fragmentation, may require the system to reorder cells ....

D. Bertsekas and R. Gallager, Data Networks, New Jersey: Prentice Hall, 1992.

....C2 T l = 1 C l Gammaf l f l C l 1 f l C l , where C l is the capacity of link l. Functions that comply with the above assumptions shall be referred to as type C functions. Such delay functions are broadly used in modeling the behavior of links in computer communication networks [23, 24]. 7 2.2 Uniqueness of the Nash Equilibrium The following result establishes the uniqueness of the NEP for the parallel lines network. Theorem 2.1 In a network of parallel links where the cost function of each user is of type A the NEP f is unique. Proof : Let f 2 F and f 2 F be two NEPs. ....

D. Bertsekas and R. Gallager, Data Networks. New-Jersey: Prentice Hall, Inc., 1987.

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D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

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D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

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D. Bertsekas and R. Gallager, Data Networks. New-Jersey: Prentice Hall, Inc., 1987.

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D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

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D. Bertsekas and R. Gallager, Data Networks. Englewood Cli#s, New Jersey: Prentice-Hall, 1987.

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D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

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D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

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D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 1987.

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D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, New Jersey: Prentice-Hall, 2nd ed., 1992.

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D. Bertsekas and R. Gallager, Data Networks, Englewood Cliffs, New Jersey:Prentice-Hall, 2nd Ed 1992.

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