fpqn

Finite-Point Queueing Network (fpqn) is a class of discrete-event models used to analyze networks of service stations that have finite buffer capacity. In an fpqn, the system is represented as a directed graph where each node denotes a service station with a limited queue, and each arc specifies the probability of customers moving from one station to another after service. Each node i has a capacity c_i and a service rate μ_i; after service completion, an item follows the routing matrix P to the next node. If the target node’s buffer is full, departures may be blocked or delayed depending on the chosen blocking discipline, which can affect overall throughput and delay.

Fpqns can be open or closed. In open networks, external arrivals feed the system and external departures remove items; in closed networks, a fixed total number of customers circulates among the nodes. The finite capacity introduces blocking and congestion effects that are not present in infinite-buffer models, making analysis more complex.

Analysis and solution methods for fpqns typically combine approximation and simulation. Exact product-form solutions are limited to special cases, while common approaches include mean value analysis adaptations for finite buffers, decomposition techniques, and discrete-event simulation. Performance measures of interest include throughput, average queue length, waiting time, utilization of stations, and the probability of blocking.

Applications of fpqns appear in manufacturing and logistics, telecommunications, and service operations where buffer sizes are constrained or costs of delay are high. They support capacity planning, buffer sizing, and policy evaluation under realistic resource limits, with the caveat that large or highly interconnected networks may require substantial computational effort.