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1993-09-22
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______________________________________________________________________________
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
On Queue
The Queueing Analysis, Simulation and Animation Program
By Victor Elias
______________________________________________________________________________
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.................................Introduction.................................
On Queue - The Queueing Analysis, Simulation and Animation Program - is
designed to make learning fun. Introductory queuing analysis is taught through
animation. Simulation is observed as "happy customers" arrive for service and
depart. Unlike any other program for queueing analysis, On Queue uses user
supplied random variables, simulates and animates the activity, and provides a
full post simulation report, and optimization analysis. On Queue also has
"word problem" solving capability in its integrated queueing equation solver.
..............................................................................
............................. System Requirements.............................
IBM or compatible computer
256k of ram
CGA or better monitor (others not tested) set to standard 80wide x 25high.
Device driver - Ansi.sys
(Install Ansi.sys by including a line, such as, device=c:\dos\ansi.sys
in the config.sys file. See your DOS manual for more instructions.)
..............................................................................
.................Queueing Analysis, Simulation and Animation..................
FEATURES COMMON TO ALL MODELS_________________________________________________
User definable Arrival Rate (random or non-random)
User definable Service Rate for each server (random or non-random)
User definable Population sample size
Animation of each customer arrival, service, departure and delay in queue
Variable animation speed for process analysis
Print out of time of each customer arrival, service, departure and delay in
queue
Post Simulation Report summarizing the actual patterns of behavior observed
in each model
Arrival distribution graph(s) and Chi-Square Goodness of Fit Test(s) for
Poisson Distribution
Service Distribution graph(s) and Chi-Square Goodness of Fit Test(s) for
Exponential Distribution
Automatic class range determination and resizing & text mode graphics
Comprehensive sample of each model - ready to run
Context sensitive help
______________________________________________________________________________
FEATURES______________________________________________________________________
Single Server Single Stage - M/M/1
Post Simulation Report
Arrival rate
Service rate
Server utilization rate
Longest service time
Shortest service time
Maximum size of queue
Interarrival time sample variance
Interarrival time sample standard deviation
Optimal service rate
Projected Steady State Server Statistics :
Arrival Rate . . . . . . . . . LAMBDA
Service Rate . . . . . . . . . MU
Server Utilization . . . . . . RHO
Length in system . . . . . . . . . Ls
Length in queue. . . . . . . . . . Lq
Length in busy queue . . . . . . . Lb
Wait in system . . . . . . . . . . . . Ws
Wait in queue. . . . . . . . . . . . . Wq
Wait in busy queue . . . . . . . . . . Wb
Variance of length in system . . . . . . . Vls
Standard Deviation, of length in system. . sqrt(Vls)
Variance of wait in system . . . . . . . . . . Vws
Standard Deviation of wait in system . . . . . sqrt(Vws)
Probability of no arrivals to system . . . . . . . Po
Probability of busy system . . . . . . . . . . . . Pb
Multiple Servers in Series
Independent queues for each server
Post Simulation Report
Arrival rate for each server
Service rate for each server
Server utilization rate for each server
Longest service time for each server
Shortest service time for each server
Average service rate
Average server utilization
Maximum size of queue for each server
Backlog server identification for process analysis & optimization
Interarrival time sample standard deviation
Interarrival time sample variance
Multiple Servers in Parallel - M/M/c
Shared queue for both servers
Post Simulation Report
Arrival rate
Service rate - for each server
Combined service rate and average service rate
Server utilization rate - for each server
Average server utilization rate
Longest service time for each server
Shortest service time for each server
Longest wait in the queue
Maximum size of queue
Number of customers sent through the queue
Arrival rate sample variance
Arrival rate sample standard deviation
Optimal number of servers
Projected Steady State Server Statistics :
Arrival Rate . . . . . . . . . LAMBDA
Service Rate . . . . . . . . . MU
Server Utilization . . . . . . RHO
Length in system . . . . . . . . . Ls
Length in queue. . . . . . . . . . Lq
Length in busy queue . . . . . . . Lb
Wait in system . . . . . . . . . . . . Ws
Wait in queue. . . . . . . . . . . . . Wq
Wait in busy queue . . . . . . . . . . Wb
Variance of length in system . . . . . . . Vls
Standard Deviation, of length in system. . sqrt(Vls)
Variance of wait in system . . . . . . . . . . Vws
Standard Deviation of wait in system . . . . . sqrt(Vws)
Probability of no arrivals to system . . . . . . . Po
Probability of busy system . . . . . . . . . . . . Pb
Economic Service Optimization
Analysis of total cost of service for up to twenty servers.
______________________________________________________________________________
..............................................................................
.............................Solving Other Models.............................
FEATURES______________________________________________________________________
Solves M/M/1 queuing problems
Poisson arrivals with exponential service time & a single server
(steady state)
Solves M/M/c queuing problems
Poisson arrivals with exponential service time & multiple servers
in parallel (steady state)
Calculates, for as many as seventy-seven servers:
Arrival rate
Service rate
Traffic intensity
Expected number of customers in the system
Expected number of customers in the queue
Expected number of customers in the queue for a busy system
Expected time in the system
Expected time in the queue
Expected time in the queue for a busy system
Variance of number of customers in the system
Standard Deviation of number of customers in the system
Variance of time in the system
Standard Deviation of time in the system
Probability of an idle system, Customer loss ratio
Economic Service Optimization
Analysis of total cost of service for up to twenty servers.
______________________________________________________________________________
..............................................................................
.................................Registration.................................
On Queue is distributed as "shareware." Please feel free to copy this
shareware edition for anyone who may be interested in trying it out. This
"read.me" file must accompany the "OnQ.exe" and "Question.txt" files and
comprises the set of On Queue software. The author accepts no responsibility
for the consequenses of your use of this program. Since On Queue was
designed, primarily, as a teaching tool, students and teachers should
register this program as soon as it is used. If you use On Queue, even for a
homework assignment, you are required to pay the registration fee. Thank you
for helping me to learn queueing analysis, simulation, animation and
programming by supporting the On Queue program through the shareware concept.
I am planning to complete several enhancements to On Queue. Such as:
1) Automatic random number generation.
2) Monte Carlo Simulation.
3) Extended Distribution analysis.
4) Extended Economic analysis and optimization.
5) Extensions of the current models - more stages & more servers.
6) File operations to save random numbers and reports.
7) An integrated employee scheduling application.
8) A guide to Statistical Quality Control, using On Queue, for service
industries.
The registration fee of $20.00 is appreciated.
For an additional $5.00 I will send you either an enhanced version of
On Queue, which is capable of modeling 50 or more customer arrivals, or I
will send you the most current shareware version of On Queue. I will also
send you the On Queue User's Guide, with a listing of standard queueing
formulas and their useage in On Queue, and solutions to questions in the On
Queue Question Set. Instructors may request a copy of the Test Bank, with
transparency masters, to accompany On Queue, for $5.00. Current copies of the
shareware version of On Queue are available for $5.00. Add $0.50 if
requesting 3.5" disks.
(California residents please include sales tax.)
Victor Elias
P.O. Box 1154
El Granada, CA 94018
If you have any suggestions or comments I'd be glad to hear from you.
Copyright 1993 Victor Elias, all rights reserved
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