Optimal design of centralized computer networks

Frank, H.; Frisch, I.; Slyke, Richard Van; Chou, Wushow

doi:10.1002/net.3230010105

Cited by 66 publications

(19 citation statements)

References 7 publications

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“…Many techniques have been proposed for centralized networks that required tree topologies [13]. In distributed systems, no efficient and exact solutions have been found for the minimum cost topology design problem.…”

Section: Related Workmentioning

confidence: 99%

Switch Scheduling and Network Design for Real-Time Systems

Gopalakrishnan

Caccamo

Sha

12th IEEE Real-Time and Embedded Technology and Applications Symposium (RTAS'06)

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The rapid need for high bandwidth and low latency communication in distributed real-time systems is driving system architects towards high-speed switches developed for high volume data transfer on the Internet. These switches employ complex scheduling algorithms for transferring data cells from the input line to the output line. From a real-time systems perspective, it is necessary to understand the behavior of these switching algorithms and obtain worst-case delay bounds for message transfer across these switches. Many researchers have derived average-case delay bounds for switching algorithms but mission-critical systems require guarantees for the worst-case. In this context, we derive upper bounds on cell delays across commonly available switches. Our bounds provide a starting point for research in this direction. Moreover, we use the delay bounds to construct low-cost networks of switches given a set of processors and their real-time communication requirements. Experiments with the heuristic algorithm that we propose for network design have produced encouraging results. Importantly, the algorithm is independent of the delay analysis technique and better techniques can be incorporated trivially. By addressing the network design problem, we hope to transform the system architecting process from a manual, ad-hoc operation to a simple and automated step that will result in better designs and cost savings.

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Section: Related Workmentioning

confidence: 99%

Switch Scheduling and Network Design for Real-Time Systems

Gopalakrishnan

Caccamo

Sha

12th IEEE Real-Time and Embedded Technology and Applications Symposium (RTAS'06)

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“…Then the nodes N -e are called free nodes. The free link ( i , j ) , used in partitioning the subset s, is chosen so that j E e. I n this way we can immediately calculate the traffic2 7 f i e 3 due to the established nodes and from the loading constraint determine whether there are any feasible solutions in the subset SI.…”

Section: Comments'mentioning

confidence: 99%

Topological Design of Multipoint Teleprocessing Networks

Elias

Ferguson

1974

IEEE Trans. Commun.

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This paper is concerned with the problem of designing a minimum-cost network of acceptable performance that connects several remote terminals to a central processor using multidrop lines. It is assumed that the message generation rate at each of the 1 terminals is known and that the communication lines of the network have the same capacity. A simple model of the network is used to derive performance constraints for the design procedure. A new heuristic design procedure is proposed. This procedure is compared to other heuristic methods and is found superior in some cases. An improved version of the branch-and-bound (BB) algorithm ofChandy and Russell is developed and tested.

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Section: Suppose That We Have Calculated the Bounds Zi And £(Sjmentioning

confidence: 99%

“…(14) If the f(n,g) corresponding to dominated solutions are eliminated at the end of (or during) each stage n, then (13) and (14) will yield the set of objective function values [f(N,P)| g € F } of the complete f ami ly of undominated feasible solutions to the (NKP) . Notice that the functional equations, (13) and (14) together with the dominance elimination, are equivalent to (1) and (2) with y^= (0,0), (15). Let u(n,3) be an upper bound on the value of an optimal solution to the residual subproblem (15 Notice that this alternative could also be broadly interpreted as using dynamic programming within a branch -and -bound framework since the dominance elimination is analogous to the initial fathoming which is employed in conventional dynamic programming.…”

Section: Suppose That We Have Calculated the Bounds Zi And £(Sjmentioning

confidence: 99%

Branch-and-Bound Strategies for Dynamic Programming

Morin

Marsten

1976

Operations Research

145

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This paper shows how branch -and -bound methods can be used to reduce storage and, possibly, computational requirements in discrete dynamic programs. Relaxations and fathoming cjriteria are used to identify and to eliminate states whose corresponding subpolicies could not lead to optimal policies. The general dynamic programming/branchand-bound approach is applied to the traveling -salesman problem and the nonlinear knapsack problem. The reported computational experience demonstrates the dramatic savings in both computer storage and computational requirements which were effected utilizing the hybrid approach.Consider the following functional equation of dynamic programming for additive costs: f(y) = min {TT(y',d) + f (y ') lT(y ' ,d) = y] , y € (P. -y.)with the boundary condition f(yo) = ko (2) in which, Q is the finite nonempty state space; y-€ fi is the initial state; d € D is a decision, where D is the finite nonempty set of decisions;T: n X D -n is the transition mapping, where T(y ',d) TT(y',d) is the incremental cost that is incurred when de-cision d is applied at state y'; k_ 6 IR is the initial cost incurred in the initial state y_; and in (2) we make the convenient but unnecessary assumption that return to the initial state is not possible. The functional equation (1) In 3 3 we show that our results extend immediately to general separable cost functions and discuss the alternative viewpoint of using dynamic programming within a branch -and -bound framcwi^rk.-3- (1) represents the discrete optimization problem 9, so that we can employ (1) and (2) Prior to discussing lower bounds and our results, it will be useful to define the policy space and some of its subsets and to define the trans i'tion mapping and cost function on the policy space. [6 @i lT(y^,6)= y'}, let A"(y')^A(y') denote the set of optimal subpolicies (policies if y' € fip) for state y'. i.e., A*(y') = {6^A(y')|f(y') = k" +'rT(y ,6)}, and let x(y') denote the completion set of feasible subpolicies which when applied at state y' result in a final state, i.e., For each state y' € n we define a lower bound mapping^: Q -• IR with the property that ay')^n(y',6) V6 € x(y').Then it is easily established thatthen 6 '6^A * for an^6 ' € A*(y') and all. 6 € x(y')« Proof .Substitute (3) and (4) i€(S-j)^J with the boundary condition f(0,-) =0. (9) Notice that (8) and (9) are equivalent to (1) and (2) The major roadblocks to solving even moderate size (N > 20) traveling -salesman problems by the dynamic programming algorithm, (8) and (9) Furthermore, even though the search over permutations in (7) has essentially been reduced to a recursive search over combinations in (8) and N-1 (9), the computational effort is still on the order of N2 (the exact number being E^" J n(n-l)f^'-^^+ (N-1) = (N-l)(l + (N-2)(l + (N-2)2^'^). An upper bound on (7) is easily obtained as the weight of any tour t €^. For example, we could take the minimum of the weights of i) the tour (1,2,..., N-1, N,l) and ii) the N nearest -neighbor tours constructed by starti...

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Optimal design of centralized computer networks

Abstract: Major design probZems for centraZized computer networks

Cited by 66 publications

References 7 publications

Switch Scheduling and Network Design for Real-Time Systems

Switch Scheduling and Network Design for Real-Time Systems

Topological Design of Multipoint Teleprocessing Networks

Branch-and-Bound Strategies for Dynamic Programming

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