SIMULATION EXAMPLES QUEUEING SYSTEMS Bilkent University IE 324

SIMULATION EXAMPLES QUEUEING SYSTEMS Bilkent University - IE 324 Simulation

Queueing Systems Entities Population …… Server Waiting Line (Queue) Finite vs. Infinite One line vs. Multiple lines Bilkent University - IE 324 Simulation One server vs. multiple server

Characteristics Interarrival and Service Times Exponential (M) Deterministic (D) Erlang (E) General (G) Queue discipline First Come/In First Served/Out (FCFS/FIFO) Last Come/In First Served/Out (LCFS/LIFO) Earliest Due Date (EDD) System Capacity Number of Servers Bilkent University - IE 324 Simulation

Applications System Entity Hospital Patient Doctor, Nurse Manufacturing Customer order Machine Food Store Purchased grocery Cashier Bank Client Clerk Computer Job CPU or disk Communication Link Data Package Data Channel Bilkent University - IE 324 Simulation Server

Analysis Methods • Queueing Theory (Analytical) – IE 325 • Simulation • Performance Measures • • Average Waiting Time Maximum Waiting Time Average Number of Entities in the System Maximum Number of Entities in the System Server Utilization Average System Time Maximum System Time Bilkent University - IE 324 Simulation

Hand Simulation of G/G/1 Events: • Arrival Event • Departure Event • End Event Variables: • Q(t) : number of units in queue at time t • B(t) : number of units in server at time t • L(t) = Q(t) + B(t) : number of units in system at time t Bilkent University - IE 324 Simulation

Arrival Event Flowchart (Logical Model) Arrival event Schedule next arrival Increase number in the system NO Make server busy B(t)=1 Is server busy? L(t)=L(t)+1 YES Increase entity number in queue Q(t)=Q(t)+1 Set service time & schedule departure Bilkent University - IE 324 Simulation

Departure Event Flowchart (Logical Model) Departure event Decrease number in system Decrease number in queue Q(t)=Q(t)-1 NO Is queue empty? L(t)=L(t)-1 YES Set service time & scheduled departure for entity in service Bilkent University - IE 324 Simulation Make server idle B(t)=0

Simulation by Hand Run simulation for 20 minutes to find • Average / Max Waiting Time • Average / Max System Time • Average Queue Length • Average Utilization Assume the first arrival occurs at zero Bilkent University - IE 324 Simulation