Concepts In DiscreteEvent Simulation System A collection of

Concepts In Discrete-Event Simulation • System A collection of entities (people and machines. . ) that interact together over time for one or more goals • Model An abstract representation of a system, usually containing structural, logical or mathematical relationship that describe a system in term of state, entities and their attributes , sets, processes, … • System state A collection of variables in any time that describe the system • Entity Any object or component in system that require explicit representation (server, customer, . . . )

• Attributes The properties of an entity • List A collection of associated entities , ordered in some logical fashion (FIFO, priority, …) • Event An instantaneous occurrence that changes the state of a system • Event Notice A record of an event to occur at the current or future time (type and time) • Event List FEL (future event list) • Activity (unconditional wait) A duration of time of specified length (service time or interarrival time, … )

• Delay (conditional wait) A duration of time of unspecified indefinite length, which is not known until it ends (customer delay in waiting line) • Clock A variable representing simulated time

Activity vs. Delay • Activity – Activity is known as unconditional wait – End of an activity is an event, for this an event notice is placed in the future event list – This event is a primary event • Delay – Delay is known as conditional wait – Delays are managed by placing the entity on another list, e. g. , representing a waiting line – Completion of delay is a secondary event, but they are not placed in the future event list

Able-Baker Call center • System state LQ(t): the number of callers waiting to serve LA(t): 0 or 1 indicate Able is idle or busy LB(t): 0 or 1 indicate Baker is idle or busy • Entities • Events Neither Callers nor the servers need to be explicitly represented except in terms of state variables. Arrival event, service completion by Able or Baker • Activities Service time by Able/Baker and Inter-arrival time • Delay A caller’s waiting time in queue until Able or Baker becomes free

• Simulation and Modeling Approaches: 1. Event-Scheduling Approach 2. Process-Interaction Approach 3. Activity-Scanning Approach

Event-Scheduling Approach • A discrete-event simulation proceeds by producing a sequence of system snapshots over time • A snapshot of the system at a given time includes

Example 3. 3 DESS of Grocery-Store

• System state LQ(t): the number of customers waiting to serve LS(t): 0 or 1 indicate Server is idle or busy • Entities Neither customers nor the servers need to be explicitly represented except in terms of state variables. • Events Arrival event(A) service completion/Departure event(D) Stopping Event(E)scheduled to occur at time t • Event Notices • Activities • Delay (A, t) Arrival Event to occur at future time t (D, t) Departure Event to occur at future time t (E, t) Stopping Event to occur at future time t Service time Inter-arrival time Time customer spend in waiting line

• Entities (Ci, t ), representing customer Ci who arrived at time t • Event notices (A , t , Ci ), the arrival of customer Ci at future time t (D, t , Cj ), the departure of customer Cj at future time t • Set : CHECKOUTLINE, the set of all customers currently at the checkout • counter (being served or waiting to be served), ordered by time of arrival

Process Approach of Modeling