# Package nl.tudelft.simulation.dsol.tutorial.section41

Simulation model of a single server system.

This section reveals the DSOL implementation of the single server queuing system. We consider a system consisting of a single server which receives customers arriving independently and identically distributed (IDD). A customer who arrives and finds the server idle is being serviced immediately. A customer who finds the server busy enters a single queue. Upon completing a service for a customer, the server checks the queue and (if any) services the next customer in a first-in, first-out (FIFO) manner.

The simulation begins in an empty-and-idle state. We simulate until a predefined fixed number of customers n have entered the system and completed their service. To measure the performance of this system, we focus on a number of output variables. First of all we focus on the expected delay d(n) of a customer in the queue. From a system perspective we furthermore focus on the number of customers in queue q(n). The final output variable we consider is the expected utilization of the server u(n). This is the proportion of the time the server was in its busy state. Since the simulation is dependent on random variable observations for both the inter-arrival time and the service time, the output variables d(n), q(n) and u(n) will be random and, therefore, expected to be variable.

Copyright (c) 2002-2020 Delft University of Technology, Jaffalaan 5, 2628 BX Delft, the Netherlands. All rights reserved. See for project information https://simulation.tudelft.nl. The DSOL project is distributed under a three-clause BSD-style license, which can be found at https://simulation.tudelft.nl/dsol/3.0/license.html.

Author:
  Peter Jacobs, Alexander Verbraeck

Class Summary
MM1Queue41Application: Copyright (c) 2002-2020 Delft University of Technology, Jaffalaan 5, 2628 BX Delft, the Netherlands.
MM1Queue41Model: The M/M/1 example as published in Simulation Modeling and Analysis by A.M.
MM1Queue41Panel: Copyright (c) 2002-2020 Delft University of Technology, Jaffalaan 5, 2628 BX Delft, the Netherlands.
MM1Queue41SwingApplication: M/M/1 queuing model with animation and graphs.
MM1Queue41SwingApplicationEvents: M/M/1 Swing application that shows the events that are fired by the Simulator in the Console.
MM1Queue41SwingApplicationEvents.SimulatorEventLogger: Class to catch the events from the Simulator to check that they are right.