Calls-for-service demand and queueing-based staffing

CallDemandModel: Poisson harmonic regression of hourly calls with daily, weekly and annual cycles and a trend (IRLS with the glm convergence rule), with forecasts. ErlangC: probability of waiting. StaffingRequirement: minimal units per period for a waiting probability, service level or mean-wait target, with optional square-root staffing. PatrolCarRequirement: PCAM-style maximum of queueing, response-time and patrol-frequency requirements. Identical to the Python arm morie.fn.staffing.

Usage

CallDemandModel(
  counts,
  hours,
  daily = 3,
  weekly = 2,
  annual = 2,
  trend = TRUE,
  new_hours = NULL,
  maxit = 100,
  epsilon = 1e-10
)

ErlangC(c, a)

StaffingRequirement(
  arrival_rates,
  handle_time,
  target = "wait_prob",
  level = 0.2,
  threshold = 0,
  beta = NULL
)

PatrolCarRequirement(
  arrival_rate,
  handle_time,
  area,
  response_speed,
  target_response,
  street_miles = 0,
  patrol_speed = 1,
  patrol_frequency = 0,
  target_wait = 0.2,
  metric = "euclidean"
)

Arguments

counts: Hourly call counts.
hours: Hour indices.
daily, weekly, annual: Numbers of harmonics.
trend: Include a linear trend.
new_hours: Hours to forecast.
maxit, epsilon: IRLS controls.
c: Number of servers.
a: Offered load.
arrival_rates, arrival_rate: Calls per hour.
handle_time: Mean handling time (hours).
target: "wait_prob", "service_level" or "asa".
level: Target value.
threshold: Service-level answer time.
beta: Square-root staffing parameter.
area: Beat area.
response_speed: Response speed.
target_response: Target travel time.
street_miles: Street length to patrol.
patrol_speed: Patrol speed.
patrol_frequency: Required passes per hour.
target_wait: Target waiting probability.
metric: "euclidean" or "rectilinear".

Value

List or numeric.

References

Green, L. V., Kolesar, P. J. and Whitt, W. (2007). Coping with time-varying demand when setting staffing requirements for a service system. Production and Operations Management 16, 13-39.

Chaiken, J. M. and Dormont, P. (1978). A patrol car allocation model: background. Management Science 24, 1280-1290.

Wilson, J. M. and Weiss, A. (2012). A Performance-Based Approach to Police Staffing and Allocation. U.S. Department of Justice, COPS Office.

Examples

ErlangC(3, 2)
#> [1] 0.4444444
StaffingRequirement(c(1, 4), 1, level = 0.2)$units
#> [1] 3 7