Service requirement 2026-11-05
A service requirement is the amount of work a job needs from a server. Queueing theory often measures that work in units of service time at full server capacity. Under this normalization, a job with service requirement needs units of uninterrupted full-capacity service; waiting before service contributes to queueing delay, not to .
If work is measured separately and a server supplies work units per second, a job requiring work units has full-capacity service time . Six work units at two units per second require three seconds of service. Under processor sharing, interruptions or partial capacity can increase elapsed completion time without increasing the original service requirement. With normalized allocated capacity , completion occurs once reaches . A residual service time describes the unserved portion, rather than a fresh draw of the original service requirement.
Service time Created 2026-10-07 Updated 2026-11-05
A service time is the time needed to complete a customer's service requirement when a server works on that customer at the declared full capacity. If the required work is and capacity is , then . Its expected value is a duration. In an M/M/1 queue, the parameter of the exponential distribution has units of inverse time, and .
Under uninterrupted first come first served, the customer's time in service equals , while its customer sojourn time also includes the preceding queueing delay. Under processor sharing, elapsed time can be longer than because each customer receives only a fraction of the capacity. For example, two jobs arriving together, each requiring six work units, finish after four seconds on a three-unit-per-second sharing server; each has full-capacity service time two seconds.
A residual service time is the remaining full-capacity service duration. Service-time variability affects the Pollaczek-Khinchine mean formula, whereas Little's law needs the relevant finite means and consistent system boundaries rather than an exponential service distribution.