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SIMULATION EXAMPLES. QUEUEING SYSTEMS. Queueing Systems. Entities. Population. ……. Server. Waiting Line (Queue). Finite vs. Infinite. One server vs. multiple server. One line vs. Multiple lines. Characteristics. Interarrival and Service Times Exponential (M) Deterministic (D)

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simulation examples

SIMULATION EXAMPLES

QUEUEING SYSTEMS

queueing systems
Queueing Systems

Entities

Population

……

Server

Waiting Line (Queue)

Finite vs.

Infinite

One server vs.

multiple server

One line vs.

Multiple lines

characteristics
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
applications
Applications

System Entity Server

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

analysis methods
Analysis Methods
  • Queueing Theory (Analytical)
  • 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
spreadsheet example
Spreadsheet Example
  • M/U/1 Simulation : Determine waiting time in queue
  • Lindley’s Formula

WQi : waiting time in queue for customer i

Si : service time for customer i

IAi : interarrival time between customers i-1 and i

hand simulation of g g 1
Hand Simulation of G/G/1

Events:

  • Arrival Event – entry of a unit into the system
  • Departure Event – completion of service on a unit
  • End Event – end of simulation

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
arrival event flowchart
Arrival Event Flowchart

Arrival event

Schedule next arrival

Increase number in the system

L(t)=L(t)+1

Is

server

busy?

NO

YES

Make server busy

Increase entity number

in queue

B(t)=1

Q(t)=Q(t)+1

Set service time &

schedule departure

departure event flowchart
Departure Event Flowchart

Departure event

Decrease number in system

L(t)=L(t)-1

NO

Is

queue

empty?

YES

Decrease number in

queue

Make server idle

Q(t)=Q(t)-1

B(t)=0

Set service time &

scheduled departure for

entity in service

simulation by hand
Simulation by Hand
  • Run simulation for 20 minutes to find
  • Average Waiting Time
  • Average Queue Length
  • Average Utilization
  • Assume the first arrival occurs at zero
finishing up
Finishing Up
  • Average waiting time in queue:
  • Time-average number in queue:
  • Utilization of drill press: