QCalc Help

QCalc computes performance measures for waiting-line 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)



Service rate









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 1-4

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 waiting-line 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.

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