Simulation modeling with event graphs

Abstract

Statistical Computing fU)bert Sargent

Perspectives on the Evolution of Simulation

“…For the latter, the activity-cycle diagram served several SPLs and was the basis for the interactive program generation work in the United Kingdom in the 1970s. Event Graphs were introduced by Schruben (1983) to assist in model building using the event world view and further developed by Sargent (1988) and Som and Sargent (1989). (We note that a representation similar to event graphs was introduced in Evans et al 1967, but apparently not further developed.…”

Intractability results in discrete-event simulation

“…This would be an important issue, for instance, in capacitated queueing Systems, queueing Systems with state-dependent routing as well as preemptive and non-preemptive priority and multiple customer-class queueing Systems. Schruben (1983) and Sargent (1988) propose rules of thumb to signal potential problems with simultaneously scheduled events. Som and Sargent (1989) develop conditions to identify when event exécution priorities need to be established.…”

Modelling and Analysis of Distributed Simulation Protocols with Distributed Graph Transformation

“…In this section we briefly present event graphs [15]. In this formalism, events are depicted as nodes in a graph.…”

“…[1] LocalVirtualTime.time = 0 // Simulation time for component [2] EventQueue.first = Initial Event // Event queue is initially empty [3] for all i in InputPort: i.clock = 0 // Set clocks for each port to 0 [4] ExecutionPointer.STEP() // Do one step, inserting internal events in queue [5] while LocalVirtualTime.timeHorizon < LocalVirtualTime.finalTime: // loop until simulation final time [6] for all i in InputPort: await not_empty(i) // wait for an event in the input port [7] for all i in InputPort: i.clock=max_timeStamp(i) // i.clock is the bigger timeStamp of any event in i [8] LocalVirtualTime.timeHorizon=min(i.clock for i in InputPort) // The process time horizon is the smaller clock of all ports [9] min_channel_id = i such that its clock is the smallest [10] if (Event.Queue.first.scheduledTime <= LocalVirtualTime.timeHorizon) [11] or (InputPort [min_channel_id].first.scheduledTime <= [12] LocalVirtualTime.timeHorizon): [13] if (Event.Queue.first.scheduledTime < [14] InputPort [min_channel_id].first.scheduledTime): [15] event = removeFirst(Event.Queue) [16] else In conservative protocols, LPs have a time horizon, which is the maximum simulation time it is safe to reach. Beyond this point causality errors may occur with incoming events.…”

“…In this approach, event classes are defined with the effects of the event on the system state and in the future (as new events can be scheduled). One of the event-scheduling modelling languages is event graphs [15], which we extended and formalized in [12] and use in this work.…”