Queueing Processes

A queueing process is a model of waiting lines, constructed so that queue length and waiting times can be predicted. Networks of connected queues allow similar models for more complex situations where routing between queues plays a role. Queues are used frequently in man-made systems, including communications (network routing, packet switching, ), computers (server scheduling, workload scheduling, ), customer service (call center, technical support, ), and health care (surgery scheduling, emergency room management, ).  The Wolfram Language provides complete support for individual queues and networks of queues. The symbolic representation of a queueing process makes it easy to simulate its behavior, estimate its parameters from data, and compute state probabilities at finite and infinite time horizons. Standard performance measures such as average waiting time or queue size are directly available.

Queueing Process Models

QueueingProcess represents a queue with general arrival and service distributions

QueueingNetworkProcess represents a network of connected queues

Performance Measures

QueueProperties steady-state and other properties for queues

ErlangB  ▪  ErlangC

Arrival and Service Distributions

ExponentialDistribution Markovian arrival or service distribution

ErlangDistribution phase-type arrival or service distribution

HypoexponentialDistribution  ▪  HyperexponentialDistribution  ▪  CoxianDistribution  ▪  GammaDistribution

Random Process Framework »

RandomFunction simulate a queueing system

EstimatedProcess estimate parameters in a queueing system

StationaryDistribution  ▪  CovarianceFunction

Related Processes

PoissonProcess  ▪  ContinuousMarkovProcess