Teunis J. Ott

Load-balancing heuristics and process behavior

Dynamic load balancing in a system of loosely-coupled homogeneous processors may employ both judicious initial placement of processes and migration of existing processes to processors with fewer resident processes. In order to predict the possible benefits of these dynamic assignment techniques, we analyzed the behavior (CPU, disk, and memory use) of 9.5 million Unix* processes during normal use. The observed process behavior was then used to drive simulation studies of particular dynamic assignment heuristics. Let <italic>F</italic>(·) be the probability distribution of the amount of CPU time used by an arbitrary process. In the environment studied we found:<list><item>(1-<italic>F</italic>(<italic>x</italic>)) ≉ <italic>rx</italic><supscrpt>-<italic>c</italic></supscrpt>, 1.05<<italic>c</italic><1.25. </item><item><italic>F</italic>(·) is far enough from exponential to make exponential models of little use. </item><item>With a foreground-background process scheduling policy in each processor, simple heuristics for initial placement and processor migration can significantly improve the response ratios of processes that demand exceptional amounts of CPU, without harming the response ratios of ordinary processes. </item></list>

A scheme for smoothing delay-sensitive traffic offered to ATM networks

The authors present a scheme for smoothing delay-sensitive traffic offered to an asynchronous transfer mode (ATM) network. They outline such a smoothing scheme, which, when applied to variable bit rate (VBR) coded video traffic, is both optimal and avoids violation of delay constraints. The scheme is based on the assumption that recent behavior of the traffic stream can be used to predict the behavior of the input stream in the near future. The effectiveness of the scheme was evaluated by simulation. The conclusion is that even with a rudimentary forecasting rule, smoothing can lower cell losses and increase the effectiveness of VBR schemes for video transmission.<<ETX>>

Efficient simulation of finite automata by neural nets

Let <italic>K</italic>(<italic>m</italic>) denote the smallest number with the property that every <italic>m</italic>-state finite automaton can be built as a neural net using <italic>K</italic>(<italic>m</italic>) or fewer neurons. A counting argument shows that <italic>K</italic>(<italic>m</italic>) is at least &OHgr;((<italic>m</italic> log <italic>m</italic>)<supscrpt>1/3</supscrpt>), and a construction shows that <italic>K</italic>(<italic>m</italic>) is at most <italic>O</italic>(<italic>m</italic><supscrpt>3/4</supscrpt>). The counting argument and the construction allow neural nets with arbitrarily complex local structure and thus may require neurons that themselves amount to complicated networks. Mild, and in practical situations almost necessary, constraints on the local structure of the network give, again by a counting argument and a construction, lower and upper bounds for <italic>K</italic>(<italic>m</italic>) that are both linear in <italic>m</italic>.

The window distribution of idealized TCP congestion avoidance with variable packet loss

This paper analyzes the stationary behavior of the TCP congestion window performing ideal congestion avoidance when the packet loss probability is not constant, but varies as a function of the window size. By neglecting the detailed window behavior during fast recovery, we are able to derive a Markov process that is then approximated by a continuous-time, continuous state space process. The stationary distribution of this process is analyzed and derived numerically and then extrapolated to obtain the stationary distribution of the TCP window. This numerical analysis enables us to predict the behavior of the TCP congestion window when interacting with a router port performing early random drop (or random early detection) where the loss probability varies with the queue occupancy.

Path selection and bandwidth allocation in MPLS networks

Multi-protocol label switching extends the IP destination-based routing protocols to provide new and scalable routing capabilities in connectionless networks using relatively simple packet forwarding mechanisms. MPLS networks carry traffic on virtual connections called label switched paths. This paper considers path selection and bandwidth allocation in MPLS networks in order to optimize the network quality of service. The optimization is based upon the minimization of a non-linear objective function which under light load simplifies to OSPF routing with link metrics equal to the link propagation delays. The behavior under heavy load depends on the choice of certain parameters. It can essentially be made to minimize maximal expected utilization, or to maximize minimal expected weighted slacks (both over all links). Under certain circumstances it can be made to minimize the probability that a link has an instantaneous offered load larger than its transmission capacity. We present a model of an MPLS network and an algorithm which optimally distributes the traffic among a set of active paths and reserves a set of back-up paths for carrying the traffic of failed or congested paths. The algorithm is an improvement of the well-known flow deviation non-linear programming method. The algorithm is applied to compute optimal LSPs for a 100-node network carrying a single traffic class. A link carrying some 1400 routes fails. The back-up paths are activated and we compare the performance of the path sets before and after the back-up paths are deployed.

On the Choice of Alternative Measures in Importance Sampling with Markov Chains

In the simulation of Markov chains, importance sampling involves replacing the original transition matrix, say P, with a suitably chosen transition matrix Q that tends to visit the states of interest more frequently. The likelihood ratio of P relative to Q is an important random variable in the importance sampling method. It always has expectation one, and for any interesting pair of transition matrices P and Q, there is a sample path length that causes the likelihood ratio to be close to zero with probability close to one. This may cause the variance of the importance sampling estimator to be larger than the variance of the traditional estimator. We develop sufficient conditions for ensuring the tightness of the distribution of the logarithm of the likelihood ratio for all sample path lengths, and we show that when these conditions are satisfied, the likelihood ratio is approximately lognormally distributed with expected value one. These conditions can be used to eliminate some choices of the alternative transition matrix Q that are likely to result in a variance increase. We also show that if the likelihood ratio is to remain well behaved for all sample path lengths, the alternative transition matrix Q has to approach the original transition matrix P as the sample path length increases. The practical significance of this result is that importance sampling can be difficult to apply successfully in simulations that involve long sample paths.

Time-segmentation parallel simulation of networks of queues with loss or communication blocking

This article is concerned with the efficient simulation of communication systems on parallel processors. In most of the article, we assume that the communication system under study can be modeled as a system of finite exponential queues with a general topology (in particular, the system need not be acyclic) and with either loss or communication blocking. We also assume that to estimate the performance measures of interest, it is necessary to generate long sample paths of the system. This is the case in both steady-state simulations and in long transient simulations. The approach involves applying each processor to simulate the entire system for a part of the time horizon of interest. We present theory guaranteeing the validity of the proposed approach, and numerical results proving the viability of the approach. The proof of the validity of the approach uses the fact that the queueing systems considered are continuous time Markov chains. An essential part of the argument is a proof that sample paths starting from different initial states eventually will couple (i.e., become identical), and a simple method for recognizing the time when a sample path has become independent of the original starting state (i.e., when all sample paths have coupled, regardless of the initial state). Finally, we discuss how our approach can be used for parallel trace-driven simulations of certain nonMarkovian systems, and state the implications of this research for the initialization bias problem in steady-state simulation.

Variance reduction through smoothing and control variates for Markov chain simulations

We consider the simulation of a discrete Markov chain that is so large that numerical solution of the steady-state balance equations cannot be done with available computers, We propose smoothing methods to obtain variance reduction when simulation is used to estimate a function of a subset of the steady-state probabilities. These methods attempt to make each transition provide information about the probabilities of interest. We give an algorithm that converges to the optimal smoothing operator, and some guidelines for picking the parameters of this algorithm. Analytical arguments are used to justify our procedures, and they are buttressed by the results of a numerical example,

TCP over ATM: ABR or UBR?

This paper reports on a simulation study of the relative performances of the ATM ABR and UBR service categories in transporting TCP/IP flows through an ATM Network. The objective is two-fold: (i) to understand the interaction between the window - based end-to-end flowcontrol TCP and the rate based flowcontrol ABR which is restricted to the ATM part of the network, and (ii) to decide whether the greater complexity of ABR (than UBR) pays off in better performance of ABR (than UBR).The most important conclusion is that there does not seem to be strong evidence that for TCP/IP workloads the greater complexity of ABR pays off in better performance.

Effect of exponential averaging on the variability of a RED queue

The paper analyzes how using a longer memory of the past queue occupancy in computing the average queue occupancy affects the stability and variability of a RED queue. Extensive simulation studies with both persistent and Web TCP sources are used to study the variance of the RED queue as a function of the memory of the averaging process. Our results show that there is very little performance improvement (and in fact, possibly significant performance degradation) if the length of memory is increased beyond a very small value. Contrary to current practice, our results show that a longer memory reduces the negative correlation typically observed among the windows of the constituent TCP flows, and hence, suggest the use of the instantaneous queue occupancy in practical RED queues.