14440312
Fluid Simulation of Large Scale Networks: Issues and Tradeoffs
Traditional discrete-event packet-level approaches to simulating computer networks become computationally infeasible as the number of network nodes or their complexity increases. An alternative approach, in which packet-level traffic sources are replaced by fluid sources, has been proposed to address this challenge. In this paper we compare the amount of computational effort needed to simulate a network using a packet-level approach versus a fluid-based approach. We quantitatively characterize the amount of computational effort needed by each approach using the notion of a simulation’s event rate, and derive expressions for the event rate of a packet and fluid flow at both the input and output sides of a queue. We show that fluid simulation can require less computational effort for simple networks. However, as the network size and complexity grow, the so-called ”ripple effect” can result in fluid simulations becoming more expensive than their packet-level counterparts. This suggests that time-driven (approximate) fluid simulation techniques may be needed to efficiently simulate large scale networks.
2853015
On the capacity of hybrid wireless networks
This paper involves the study of the throughput capacity of hybrid wireless networks. A hybrid network is formed by placing a sparse network of base stations in an ad hoc network. These base stations are assumed to be connected by a high-bandwidth wired network and act as relays for wireless nodes. They are not data sources nor data receivers. Hybrid networks present a tradeoff between traditional cellular networks and pure ad hoc networks in that data may be forwarded in a multihop fashion or through the infrastructure. It has been shown that the capacity of a random ad hoc network does not scale well with the number of nodes in the system. In this work, we consider two different routing strategies and study the scaling behavior of the throughput capacity of a hybrid network. Analytical expressions of the throughput capacity are obtained. For a hybrid network of n nodes and m base stations, the results show that if m grows asymptotically slower than √n, the benefit of adding base stations on capacity is insignificant. However, if m grows faster than √n, the throughput capacity increases linearly with the number of base stations, providing an effective improvement over a pure ad hoc network. Therefore, in order to achieve nonnegligible capacity gain, the investment in the wired infrastructure should be high enough.
800712
On the autocorrelation structure of TCP traffic
The statistical characteristics of network traffic--in particular the observation that it can exhibit long range dependence--have received considerable attention from the research community over the past few years. In addition, the recent claims that the TCP protocol can generate traffic with long range dependent behavior has also received much attention. Contrary to the latter claims, in this paper we show that the TCP protocol can generate traffic with correlation structures that spans only an analytically predictable finite range of time-scales. We identify and analyze separately the two mechanisms within TCP that are responsible for this scaling behavior: timeouts and congestion avoidance. We provide analytical models for both mechanisms that, under the proper loss probabilities, accurately predict the range in time-scales and the strength of the sustained correlation structure of the traffic sending rate of a single TCP source. We also analyze an existing comprehensive model of TCP that accounts for both mechanisms and show that TCP itself exhibits a predictable finite range of time-scales under which traffic presents sustained correlations. Our claims and results are derived from Markovian models that are supported by simulations. We note that traffic generated by TCP can be misinterpreted to have long range dependence, but that long range dependence is not possible due to inherent finite time-scales of the mechanisms of TCP.
2578283
On the efficiency of fluid simulation of networks
Performance evaluation of computer networks through tratitional packet-level simulation is becoming increasingly difficult as networks grow in size along different dimensions. Due to its higher level of abstraction, fluid simulation is a promising approach for evaluating large-scale network models. In this paper we focus on evaluating and comparing the computaional effort required for fluid-and packet-level simulation. To measure the computaional effort required by a simulation approach, we introduce the concept of "simulation event rate", a measure that is both analytically tractable and adequate. We identify the fundamental factors that contribute to the simulation event rate in fluid- and packet-level simulations and provide an analytical characterization of the simulation event rate for specific network models. Among such factors, we identify the "ripple effect" as a significant contributor to the computational effort required by fluid simulation. We also show that the parameter space of a given network model can be divided into different regions where one simulation technique is more efficient than the other. In particular, we consider a realistic large-scale network and demonstrate how the computational effort depends on simulation parameters. Finally, we show that flow aggregation can effectively reduce the impact of the ripple effect and that the ripple effect has less impact when simulating the WFQ scheduling policy.
1727263
A study of networks simulation efficiency: fluid simulation vs. packet-level simulation
Network performance evaluation through traditional packet-level simulation is becoming increasingly difficult as today's networks grow in scale along many dimensions. As a consequence, fluid simulation has been proposed to cope with the size and complexity of such systems. This study focuses on analyzing and comparing the relative efficiencies of fluid simulation and packet-level simulation for several network scenarios. We use the "simulation event" rate to measure the computational effort of the simulators and show that this measure is both adequate and accurate. For some scenarios, we derive analytical results for the simulation event rate and identify the major factors that contribute to the simulation event rate. Among these factors, the "ripple effect" is very important since it can significantly increase the fluid simulation event rate. For a tandem queueing system, we identify the boundary condition to establish regions where one simulation paradigm is more efficient than the other. Flow aggregation is considered as a technique to reduce the impact of the "ripple effect" in fluid simulation. We also show that WFQ scheduling discipline can limit the "ripple effect", making fluid simulation particularly well suited for WFQ models. Our results show that tradeoffs between parameters of a network model determines the most efficient simulation approach.
31833569
The kth Lower Multiexponent of Tournament Matrices
36301624
Some results on integral sum graphs
Abstract Let Z denote the set of all integers. The integral sum graph of a finite subset S of Z is the graph (S,E) with vertex set S and edge set E such that for u,v∈S, uv∈E if and only if u+v∈S . A graph G is called an integral sum graph if it is isomorphic to the integral sum graph of some finite subset S of Z . The integral sum number of a given graph G , denoted by ζ(G) , is the smallest number of isolated vertices which when added to G result in an integral sum graph. Let ⌈x⌉ denote the least integer not less than the real x . In this paper, we (i) determine the value of ζ(K n −E(K r )) for r⩾⌈2n/3⌉−1 , (ii) obtain a lower bound for ζ(K n −E(K r )) when 2⩽r and n⩾5 , showing by construction that the bound is sharp when r=2 , and (iii) determine the value of ζ(K r,r ) for r⩾2 . These results provide partial solutions to two problems posed by Harary (Discrete Math. 124 (1994) 101–108). Finally, we furnish a counterexample to a result on the sum number of K r,s given by Hartsfiedl and Smyth (Graphs and Matrices, R. Rees (Ed.), Marcel, Dekker, New York, 1992, pp. 205–211).
17725194
SPF: to improve the performance of packet-mode scheduling
Recent researches present that packet-mode scheduling may provide overall performance advantages over cell-mode scheduling in input queueing switches. But one significant drawback of existing packet-mode schedulers is that they tend to result in longer waiting time of short packets, whose delay is critical to the performance of IP networks. To mitigate the problem, this paper proposes a simple but effective packet-mode scheduling algorithm called Short Packets First (SPF), studies the corresponding buffering architecture, and evaluates the performance on throughput and packet delay. SPF achieves 100% throughput under an accurate Internet traffic model. Theoretical analysis proves that SPF can reduce the average packet waiting time of short packets as well as overall packets, under the condition of uniform Poisson arrival process and low to medium offered load. Furthermore, extended simulation studies show that SPF is superior to general packet-mode and cell-mode scheduling, especially under heavy offered load.
1437746
On the skew-bounded minimum-buffer routing tree problem
Bounding the load capacitance at gate outputs is a standard element in today's electrical correctness methodologies for high-speed digital very large scale integration design. Bounds on load caps improve coupling-noise immunity, reduce degradation of signal transition edges, and reduce delay uncertainty due to coupling noise (Kahng et al. 1998). For clock and test distribution, an additional design requirement is bounding the buffer skew, i.e., the difference between the maximum and the minimum number of buffers over all of the source-to-sink paths in the routing tree, since buffer skew is one of the main factors affecting delay skew (Tellez and Sarrafzadeh 1997). In this paper, we consider algorithms for buffering a given tree with the minimum number of buffers under given load cap and buffer skew constraints. We show that the greedy algorithm proposed by Tellez and Sarrafzadeh is suboptimal for nonzero buffer-skew bounds and give examples showing that no bottom-up greedy algorithm can achieve optimality. The main contribution of the paper is an optimal dynamic programming algorithm for the problem. Experiments on test cases extracted from recent industrial designs show that the dynamic programming algorithm has practical running time and saves up to 37.5% of the buffers inserted by Tellez and Sarrafzadeh's algorithm.
3063801
Iteration-Shared Scheduling Algorithms Abolishing the Departure-Time-Compatible Graph in Switch-Memory-Switch Switches
Switch-Memory-Switch (SMS) architecture exhibits an excellent performance due to its emulating the Output Queueing structure. However, in order to achieve the maximal matching, the first stage scheduling operates at a huge computational complexity, which blocks the SMS from practical implementation. In order to put SMS into more effective industrial applications, especially in super-large size switches/routers with multi-services environment, two parallel iterative scheduling algorithms, named IS-RRM and AIS-RRM respectively, are proposed in this paper. The algorithms abolish totally the traditional departure-time-compatible (DTC) graph, and by using iteration-sharing technology, greatly reduce the required iteration number in each time slot. Using a discrete-time Markov chain to model the AIS-RRM algorithm, we obtain its upper bound of cell loss rate. Meanwhile, experimental and theoretical results show that so long as the number of shared memories is twice the switch size, AIS-RRM algorithm can achieve a cell loss rate of 10 when the input buffer size is 15 and the iteration number of each time slot is 6, despite the arrival traffic pattern and the switch size. Furthermore, the iteration number required in each time slot can be further decreased by increasing the input buffer size.