HypercubeQueue: Larson (1974) hypercube queueing model (zero or
infinite line) with unit workloads, dispatch fractions, loss or waiting
probability and travel times. SquareRootLaw: Kolesar-Blum response
distance. ShortCrimeLattice: Short et al. (2008) agent burglary
model on a periodic lattice. ShortCrimePde: its continuum
reaction-diffusion version with hotspot suppression. Units and atoms are
0-based in preferences, as in the Python arm morie.fn.policeops.
Usage
HypercubeQueue(
arrival_rates,
preferences,
service_rate = 1,
queue = "zero",
travel_time = NULL
)
SquareRootLaw(area, available_units, metric = "euclidean", speed = NULL)
ShortCrimeLattice(
n,
steps,
A0 = 1/30,
eta = 0.03,
omega = 1/15,
gamma = 0.002,
B0 = NULL,
criminals = NULL,
seed = 1
)
ShortCrimePde(
B,
rho,
dx = 1,
dt = 0.01,
steps = 100,
eta = 0.03,
omega = 1/15,
A0 = 1/30,
gamma = 0.002,
D = 1,
eps = 1,
z = 4,
suppress = NULL
)Arguments
- arrival_rates
Call rates by atom.
- preferences
List of unit dispatch orders (0-based) per atom.
- service_rate
Service rate per unit.
- queue
"zero"or"infinite".- travel_time
Units x atoms travel times.
- area, available_units
Area and available units.
- metric
"euclidean"or"rectilinear".- speed
Travel speed.
- n
Lattice side.
- steps
Time steps.
- A0, eta, omega, gamma
Model parameters.
- B0
Initial dynamic attractiveness (length
n^2).- criminals
Initial criminal sites (0-based).
- seed
Philox seed.
- B, rho
Initial fields (matrices).
- dx, dt
Grid spacing and time step.
- D, eps, z
Continuum constants.
- suppress
0/1 matrix of policed cells.
References
Larson, R. C. (1974). A hypercube queuing model for facility location and redistricting in urban emergency services. Computers and Operations Research 1, 67-95.
Kolesar, P. and Blum, E. H. (1973). Square root laws for fire engine response distances. Management Science 19, 1368-1378.
Short, M. B. et al. (2008). A statistical model of criminal behavior. Mathematical Models and Methods in Applied Sciences 18, 1249-1267.