genMM1 {boodd}R Documentation

Generate an M/M/1 Queue Process

Description

Simulates an M/M/1 queue process. The M/M/1 queue is a single-server queue with Poisson arrivals and exponential service times. Allows to introduce an artificial outlier.

Usage

genMM1(n, lambda, mu, out = NULL)

Arguments

n

An integer value; the length of the process to simulate.

lambda

A positive numeric value; rate parameter for the Poisson arrival process.

mu

A positive numeric value; rate parameter for the exponential service times.

out

A positive numeric value; the value of an outlier appearing at time floor(n/2)+1. Default is NULL, this means that the process is generated without outlier.

Details

The M/M/1 waiting time is defined as follows

X_{t+1} = \max(0, (X_t + U_t - V_t))

, where U_t and V_t are exponentially distributed random variables with parameters lambda and mu, respectively.

Value

A numeric vector of length n+1, representing the waiting time of customer i arriving at time T_i.

References

Bertail, P. and Dudek, A. (2025). Bootstrap for Dependent Data, with an R package (by Bernard Desgraupes and Karolina Marek) - submitted.

Asmussen, S. (1987). Applied Probability and Queues. Springer N.Y.

See Also

genETARCH, zi_inar_process.

Examples

queue = genMM1(100,1,2) 
plot(queue, type="l")


[Package boodd version 0.1 Index]