This paper analyses the stability and fairness of two classes of rate control algorithm for communication networks. The algorithms provide natural generalisations to large-scale networks of simple additive increase/multiplicative decrease schemes, and are shown to be stable about a system optimum characterised by a proportional fairness criterion. Stability is established by showing that, with an appropriate formulation of the overall optimisation problem, the network's implicit objective function provides a Lyapunov function for the dynamical system defined by the rate control algorithm. The network's optimisation problem may be cast in primal or dual form: this leads naturally to two classes of algorithm, which may be interpreted in terms of either congestion indication feedback signals or explicit rates based on shadow prices. Both classes of algorithm may be generalised to include routing control, and provide natural implementations of proportionally fair pricing.

https://link.springer.com/content/pdf/10.1057%2Fpalgrave.jors.2600523.pdf

Rate control for communication networks: shadow prices, proportional fairness and stability

In this paper, we demonstrate the existence of fair end-to-end window-based congestion control protocols for packet-switched networks with first come-first served routers. Our definition of fairness generalizes proportional fairness and includes arbitrarily close approximations of max-min fairness. The protocols use only information that is available to end hosts and are designed to converge reasonably fast. Our study is based on a multiclass fluid model of the network. The convergence of the protocols is proved using a Lyapunov function. The technical challenge is in the practical implementation of the protocols.

https://www-inst.eecs.berkeley.edu/~ee228a/fa03/228A03/papers/Mo.pdf

Fair end-to-end window-based congestion control

Parallel discrete event simulation (PDES), sometimes called distributed simulation, refers to the execution of a single discrete event simulation program on a parallel computer. PDES has attracted a considerable amount of interest in recent years. From a pragmatic standpoint, this interest arises from the fact that large simulations in engineering, computer science, economics, and military applications, to mention a few, consume enormous amounts of time on sequential machines. From an academic point of view, parallel simulation is interesting because it represents a problem domain that often contains substantial amounts of parallelism (e.g., see [59]), yet paradoxically, is surprisingly difficult to parallelize in practice. A sufficiently general solution to the PDES problem may lead to new insights in parallel computation as a whole. Historically, the irregular, data-dependent nature of PDES programs has identified it as an application where vectorization techniques using supercomputer hardware provide little benefit [14].A discrete event simulation model assumes the system being simulated only changes state at discrete points in simulated time. The simulation model jumps from one state to another upon the occurrence of an event. For example, a simulator of a store-and-forward communication network might include state variables to indicate the length of message queues, the status of communication links (busy or idle), etc. Typical events might include arrival of a message at some node in the network, forwarding a message to another network node, component failures, etc.We are especially concerned with the simulation of asynchronous systems where events are not synchronized by a global clock, but rather, occur at irregular time intervals. For these systems, few simulator events occur at any single point in simulated time; therefore parallelization techniques based on lock-step execution using a global simulation clock perform poorly or require assumptions in the timing model that may compromise the fidelity of the simulation. Concurrent execution of events at different points in simulated time is required, but as we shall soon see, this introduces interesting synchronization problems that are at the heart of the PDES problem.This article deals with the execution of a simulation program on a parallel computer by decomposing the simulation application into a set of concurrently executing processes. For completeness, we conclude this section by mentioning other approaches to exploiting parallelism in simulation problems.Comfort and Shepard et al. have proposed using dedicated functional units to implement specific sequential simulation functions, (e.g., event list manipulation and random number generation [20, 23, 47]). This method can provide only a limited amount of speedup, however. Zhang, Zeigler, and Concepcion use the hierarchical decomposition of the simulation model to allow an event consisting of several subevents to be processed concurrently [21, 98]. A third alternative is to execute independent, sequential simulation programs on different processors [11, 39]. This replicated trials approach is useful if the simulation is largely stochastic and one is performing long simulation runs to reduce variance, or if one is attempting to simulate a specific simulation problem across a large number of different parameter settings. However, one drawback with this approach is that each processor must contain sufficient memory to hold the entire simulation. Furthermore, this approach is less suitable in a design environment where results of one experiment are used to determine the experiment that should be performed next because one must wait for a sequential execution to be completed before results are obtained.

/pdf/parallel-discrete-event-simulation-m759whzicd.pdf

Parallel discrete event simulation

Originating from basic research conducted in the 1970's and 1980's, the parallel and distributed simulation field has matured over the last few decades. Today, operational systems have been fielded for applications such as military training, analysis of communication networks, and air traffic control systems, to mention a few. The article gives an overview of technologies to distribute the execution of simulation programs over multiple computer systems. Particular emphasis is placed on synchronization (also called time management) algorithms as well as data distribution techniques.

/pdf/parallel-and-distributed-simulation-systems-2ovm9qn1cd.pdf

Parallel and Distributed Simulation Systems

/pdf/reversibility-and-stochastic-networks-17kl9p5ino.pdf

Reversibility and Stochastic Networks

This isn't the real cover. It's the one we wanted. Drawn by Freddy Bruckstein.

Large deviations for performance analysis

What this is, and what it is not Large deviations of random variables General principles Random walks, branching processes Poisson and related processes Large deviation for processes Freidlin-Wentzell theory Boundary theory Allocating independent subtasks Parallel algorithms: rollback Accelerated simulation the M/M/1 queue The Flatto-Hahn-Wright model Erlang's model The Anick-Mitra-Sondhi model ALOHA Priority queues Flatto's models Analysis and Probability Discrete-space markov processes Calculus of variations Large deviations techniques.

Large Deviations For Performance Analysis: Queues, Communication and Computing

We present a simple method of estimating the sensitivity of quantities obtained from simulation with respect to a class of parameters Here sensitivity means the derivative of an expectation with respect to a parameter The class of parameters includes, for example, Poisson rates, discrete probabilities, and the mean and variance of a Normal distribution The method is extremely well suited to regenerative simulation, and can be implemented on extant simulations with little effort, increase in running time, or memory requirements It is based on some change-of-measure formulas derived from likelihood ratios In addition to the theorems that underly the technique, we present some numerical examples

https://www.jstor.org/stable/pdfplus/171028.pdf

Sensitivity Analysis for Simulations via Likelihood Ratios

The main contributions of this paper are two-fold. First, we prove fundamental, similarly behaving lower and upper bounds, and give an approximation based on the bounds, which is effective for analyzing ATM multiplexers, even when the traffic has many, possibly heterogeneous, sources and their models are of high dimension. Second, we apply our analytic approximation to statistical models of video teleconference traffic, obtain the multiplexing system's capacity as determined by the number of admissible sources for given cell-loss probability, buffer size and trunk bandwidth, and, finally, compare with results from simulations, which are driven by actual data from coders. The results are surprisingly close. Our bounds are based on large deviations theory. The main assumption is that the sources are Markovian and time-reversible. Our approximation to the steady-state buffer distribution is called Chenoff-dominant eigenvalue since one parameter is obtained from Chernoffs theorem and the other is the system's dominant eigenvalue. Fast, effective techniques are given for their computation. In our application we process the output of variable bit rate coders to obtain DAR(1) source models which, while of high dimension, require only knowledge of the mean, variance, and correlation. We require cell-loss probability not to exceed 10/sup -6/, trunk bandwidth ranges from 45 to 150 Mb/s, buffer sizes are such that maximum delays range from 1 to 60 ms, and the number of coder-sources ranges from 15 to 150. Even for the largest systems, the time for analysis is a fraction of a second, while each simulation takes many hours. Thus, the real-time administration of admission control based on our analytic techniques is feasible. >

Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing

A variety of theoretical results are derived for a well-known class of discrete-time adaptive filters. First the following idealized identification problem is considered: a discrete-time system has vector input x(t) and scalar output z(t)= h \' x(t) where h is an unknown time-invariant coefficient vector. The filter considered adjusts an estimate vector \hat{h}(t) in a control loop according to \hat{h}(t + \Delta t) = \hat{h}(t) + K[z(t) - \hat{z} (t)]x(t) , where \hat{z}( t)= \hat{h}( t) \' x( t) and K is the control loop gain. The effectiveness of the filter is determined by the convergence properties of the misalignment vector r(t) = h - \hat{h}(t) . It is shown that a certain nondegeneracy "mixing" condition on the Input { x(t)} is necessary and sufficient for the exponential convergence of the misalignment. Qualitatively identical upper and lower bounds are derived for the rate of convergence. Situations where noise is present in z(t) and x(t) and the coefficient vector h is time-varying are analyzed. Nonmixing inputs are also considered, and it is shown that in the idealized model the above stability results apply with only minor modifications. However, nonmixing input in conjunction with certain types of noise lead to bounded input - unbounded output, i.e., instability.

Digital adaptive filters: Conditions for convergence, rates of convergence, effects of noise and errors arising from the implementation

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