QCalc computes performance measures for waitingline systems of the types: M/M/1, M/M/s, M/D/1, and M/M/1 with a finite population. The table below summarizes the characteristics of these queueing systems

Model 1 M/M/1

Model 2 M/M/s

Model 3 M/D/1

Model 4 M/M/1 finite population

# channels, s

Single, s=1

Multiple (s)

Single

Single

Service rate

Exponential

Exponential

Constant

Exponential

Population

Infinite

Infinite

Infinite

Limited (size m)


User inputs (all models)
 Model title: Descriptive title for reports
 Arrival rate, lambda (l): the average number of customers arriving for service per time period. Examples: 3.4 cars arrive per minute, 45.1 people per hour call for information
 Service rate, mu (m): average number of customers that one server can process per period. Examples: car wash can clean 19.8 cars per hour, web server can deliver 2000 page requests per minute
 Model choice: selection of model 14
User input (specific models)
 Model 2: s, the number of parallel servers. Examples: number of grocery checkout lanes, number of operators in a call center
 Model 4: m, the size of the population from which the arrivals emanate. Examples: the number of copy machines that might need repair, the number of students authorized to use the power engineering laboratory.
Generated output
When the “Compute statistics” button is selected, Qcalc computes and displays a report with:
 List of assumptions about the waitingline system being analyzed
 Measures of effectiveness of system performance
 Individual and cumulative probabilities of i customers in the system, either waiting or being served, for i = 0 to 14. That is, Pi and S Pj, for j = 0 ... i
See Barr, Production Systems Handbook for details.
