Simulation language

Abstract: 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.

Abstract: This tutorial surveys the state of the art in executing discrete event simulation programs on a parallel computer. Specifically, we will focus attention on asynchronous simulation programs where few events occur at any single point in simulated time, necessitating the concurrent execution of events occurring at different points in time. We first describe the parallel discrete event simulation problem, and examine why it so difficult. We review several simulation strategies that have been proposed, and discuss the underlying ideas on which they are based. We critique existing approaches in order to clarify their respective strengths and weaknesses.

Abstract: Established system relationships for discrete systems, such as language inclusion, simulation, and bisimulation, require system observations to be identical. When interacting with the physical world, modeled by continuous or hybrid systems, exact relationships are restrictive and not robust. In this paper, we develop the first framework of system approximation that applies to both discrete and continuous systems by developing notions of approximate language inclusion, approximate simulation, and approximate bisimulation relations. We define a hierarchy of approximation pseudo-metrics between two systems that quantify the quality of the approximation, and capture the established exact relationships as zero sections. Our approximation framework is compositional for a synchronous composition operator. Algorithms are developed for computing the proposed pseudo-metrics, both exactly and approximately. The exact algorithms require the generalization of the fixed point algorithms for computing simulation and bisimulation relations, or dually, the solution of a static game whose cost is the so-called branching distance between the systems. Approximations for the pseudo-metrics can be obtained by considering Lyapunov-like functions called simulation and bisimulation functions. We illustrate our approximation framework in reducing the complexity of safety verification problems for both deterministic and nondeterministic continuous systems