Jeff S. Steinman
Abstract
The event horizon is a very important concept that is useful for both parallel and sequential discrete-event simulations. By exploiting the event horizon, parallel simulations can process events in a manner that is risk-free (i.e., no antimessages) in adaptable “breathing” time cycles with variable time widths. Additionally, exploiting the event horizon can greatly reduce the event list management overhead that is common to virtually all discrete-event simulations.
This paper develops an analytic model describing the event horizon from first principles using equilibrium considerations and the hold model (where each event, when consumed, generates a single new event with future-time statistics described by a known probability function). Exponential and Beta-density functions are used to verify the mathematics presented in this paper.
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Index Terms
- Discrete-event simulation and the event horizon
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Reviews
Anthony Joseph Duben
The concept of an event horizon originated in cosmology. It describes the boundary of the region in space-time from which neither matter nor energy can escape. This concept has been adapted to discrete-event simulation in order to accelerate the processing of events by reducing the overhead of maintaining the linked list in which events are stored. Two sets of events are maintained—a primary set, which is ordered in time, and a secondary set of events that are generated as the events in the primary set are processed. The secondary set is not ordered. Only the earliest event in the secondary set is identified. The time of this event is the event horizon. The primary set is processed until the event horizon is encountered, then the secondary set is sorted and merged with the remainder of the primary set, and the cycle begins again. Time is saved by reducing the overhead of continually managing a sorted list of events. Steinman provides an analytic foundation for the event horizon in discrete simulation. He begins with the event density function, the equilibrium distribution of events in the simulation, and from this determines the event-insertion bias (the fraction of the linked list that must be traversed for insertion), the average number of events that are processed in a cycle, and the average event horizon time-interval. The formalism is applied to the beta-density function, a flexible, general probability distribution that provides a large set of test cases. The brief report of the beta-density function application is the only numerical example in the paper. A major result of the analysis is the demonstration that longer lookahead (the time difference between a processed event and the event that it generates) improves the performance of parallel simulations. Although this paper is basically theoretical, it is worthy of the attention of simulation practitioners.
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