Conceptual Information Model ^?

The potentially relevant object types are:

1. customers,
2. service desks,
3. service queues,
4. service clerks.

Notice that it seems preferable (more natural) to separate the service queue from the service desk and not consider the customer that is currently being served at the service desk to be part of the queue.

Conceptually, a queue is a linearly ordered collection of objects of a certain type with a First-In-First-Out policy: the next object to be removed is the first object, at the front of the queue, while additional objects are added at the end of the queue.

Potentially relevant types of events are:

1. customer arrivals,
2. customers queuing up,
3. customers being notified/invited to move forward to the service desk,
4. service start,
5. service end,
6. customer departures.

Notice that a pair of start and end events, like "service start" and "service end", indicates that there is an activity that is temporally framed by these two events. It's an option to consider also activities, in addition to objects and events, in a conceptual model. We will do this in our 3rd simulation model of the service desk system.

Both object types and event types, together with their participation associations, can be visually described in a UML class diagram, as shown below.

Conceptual Process Model ^?

Event rules.

ON (event type)	DO (event routine)	Diagram
customer arrival	If the service desk is busy, then the new customer queues up, else the service starts.
service start	After some time, the service ends.
service end	The served customer departs. If there are still customers waiting in the queue, then the next service starts.

The involved types of events can be related with each other via their (possibly conditional) temporal succession, as visualized in the following BPMN process diagram:

Information Design Model ^?

In the given simulation project, the purpose of the simulation model is to compute only two statistics: maximum queue length and average queue length, both based on a single state variable: the length of the queue at the service desk. We may abstract away from all the object types listed in the conceptual information model and model the queue length state variable in the form of a global variable queueLength, and the service duration random variable in the form of a global function serviceDuration().

Concerning the event types described in the conceptual information model, the goal is to keep only those of them, which are really needed, in the design model. This question is closely related to the question, which types of state changes and follow-up event creation have to be modeled for being able to answer the research question(s).

In the case of the given research question, we only need to keep track of changes of the queue length. For keeping track of queue length changes, we only need to consider those types of events that may change the queue length: customer arrivals and customer departures. These are the only relevant event types.

As an exogenous event type, CustomerArrival has a recurrence function representing a random variable for computing the time in-between two subsequent event occurrences.

Notice that, for simplicity, we consider the customer that is currently being served to be part of the queue. In this way, in the simulation program, we can check if the service desk is busy by testing if the length of the queue is greater than 0.

An alternative approach would be not considering the currently served customer as part of the queue, but rather use a Boolean attribute isBusy for being able to keep track if the service desk ist still busy with serving a customer.

Process Design Model ^?

Event rule design table.

ON (event type)	DO (event routine)	Rule design model
CustomerArrival @ t	INCREMENT queueLength IF queueLength = 1 THEN SCHEDULE CustomerDeparture @ (t + serviceDuration())
CustomerDeparture @ t	DECREMENT queueLength IF queueLength > 0 THEN SCHEDULE CustomerDeparture @ (t + serviceDuration())

Other OES Models for the Same System/Problem/Domain

1. ServiceDesk-1: A service queue model (one service and one queue) with two statistics: maximum queue length and service utilization. The model includes an object type ServiceDesk, but abstracts away from individual customers and from the composition of the queue.
2. ServiceDesk-2: A service queue model (one service and one queue) with one statistic: the Mean Response Time, which is the average length of time a customer spends in the system from arrival to departure. For recording their arrival time, individual customers are represented explicitly in a waitingCustomers queue.
3. ServiceDesk-3: A service queue model where the service is modeled as an activity with the service desk as its resource, for which the utilization statistics is computed automatically.
4. ServiceDesk-4: A service queue model where the service desk is modeled as a processing node of a processing network that has an entry node and an exit node for arriving and departing customers. The model is based on the pre-defined Processing Network concepts: WorkObject, Arrival, EntryNode, ProcessingNode and ExitNode, such that processing objects 'flow through the system'.
5. ConsecutiveServices: An activity-based service queue model of two consecutive service providers with customer waiting lines.
6. ProcessingNetwork-1: A service queue model where service providers are modeled as processing nodes (with input queues) within a processing network that has an entry node and an exit node for arriving and departing customers. The model is based on the pre-defined Processing Network concepts: WorkObject, Arrival, EntryNode, ProcessingNode and ExitNode, such that processing objects 'flow through the system'.

Similar Models Implemented with Other Frameworks

1. Queueing_Simulation_Discrete_Event: This NetLogo simulation uses NetLogo's tick-advance primitive to advance simulation time by non-integral amounts. However, NetLogo's standard ticks display is unable to display non-integral values, so a custom ticks display has to be programmed. Copyright 2010, Nick Bennett.