Concepts In Discrete-Event Simulation System Model System state Entity A collection of entities (people and machines..) that interact together over time for one or more goals 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,… A collection of variables in any time that describe the system Any object or component in system that require explicit representation (server, customer,...)

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

Delay (conditional wait) Clock A duration of time of unspecified indefinite length, which is not known until it ends (customer delay in waiting line) 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 Entities Events Activities Delay 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 Neither Callers nor the servers need to be explicitly represented except in terms of state variables. Arrival event, service completion by Able or Baker Service time by Able/Baker and Inter-arrival time 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 Entities Events Event Notices Activities Delay LQ(t): the number of customers waiting to serve LS(t):0 or 1 indicate Server is idle or busy Neither customers nor the servers need to be explicitly represented except in terms of state variables. Arrival event(A) service completion/Departure event(D) Stopping Event(E)scheduled to occur at time t (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