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, ...).
Mathematica 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.
QueueingProcess — represents a queue with general arrival and service distributions
QueueingNetworkProcess — represents a network of connected queues
QueueProperties — steady-state and other properties for queues
ExponentialDistribution — Markovian arrival or service distribution
ErlangDistribution — phase-type arrival or service distribution
RandomFunction — simulate a queueing system
EstimatedProcess — estimate parameters in a queueing system