Little's law on a court docket

From the arrival and disposition times of cases (a disposition missing or after the horizon: still pending), the time-average backlog equals the filing rate times the mean time to disposition when every case has been disposed (Little 1961): resid is that identity's residual, 0 up to rounding. The backlog counts each pending case to the horizon; the mean time is over the disposed cases, which understates the truth when cases are pending (see losbnd()). Given a target backlog, need is the mean time to disposition that holds it at the present filing rate. See proof("bklog").

Usage

bklog(arrive, dispose, horizon = NULL, target = NULL)

Arguments

arrive

The arrival time of each case: numbers from 0.

dispose

The disposition time of each case: numbers, NA for one pending.

horizon

NULL (the latest arrival or disposition) or the end of the window: one positive number.

target

NULL, or a target backlog: one number from 0.

Value

An object of class bklog, a list: est, a named vector (cases, pending, rate the filing rate, wait the mean time to disposition, backlog, occup the case-time, resid); horizon; and need (with target).

References

Little, J. D. C. (1961). A proof for the queuing formula: L = lambda W. Operations Research, 9(3), 383-387. doi:10.1287/opre.9.3.383

Examples

bklog(arrive = c(0, 2, 3, 7, 9), dispose = c(5, 4, 12, NA, 15),
      horizon = 20, target = 2)
#> bklog: Little's law over a horizon of 20 
#>   cases pending    rate    wait backlog   occup   resid 
#>    5.00    1.00    0.25    5.50    1.75   35.00      NA