queues queuing system model we can model queuing system by constructing discrete event simulation the simulation is sequence of significant events that cause change in the system for examplein our airline ticket counter simulationthese events would include customer arrivalthe start or conclusion of transactionor customer departure the simulation is time driven and performed over preset time period the passing of time is represented by loopwhich increments discrete time variable once for each tick of the clock the events can only occur at discrete time intervals thusthe time units must be small enough such that no event can occur between units simulation is commonly designed to allow the user to supply parameters that define the conditions of the system for discrete event simulation modeling queuing systemthese parameters includethe length of the simulation given in number of time units the simulation typically begins at time unit zero the number of servers providing the service to the customers we must have at least one server the expected service time to complete transaction the distribution of arrival timeswhich is used to determine when customers arrive by adjusting these parametersthe user can change the conditions under which the simulation is performed we can change the number of serversfor exampleto determine the optimal number required to provide satisfactory service under the given conditions finallya set of rules are defined for handling the events during each tick of the clock the specific rules depends on what results are being studied to determine the average time customers must wait in line before being servedthere are three rulesrule if customer arriveshe is added to the queue at mostone customer can arrive during each time step rule if there are customers waitingfor each free serverthe next customer in line begins her transaction rule for each server handling transactionif the transaction is completethe customer departs and the server becomes free when the simulation completesthe average waiting time can be computed by dividing the total waiting time for all customers by the total number of customers random events to correctly model queuing systemsome events must occur at random one such event is customer arrival in the first rule outlined earlierwe need to determine if