Finitecapacity

Finite capacity refers to systems or processes that have a fixed upper limit on the amount of a resource that can be held, processed, or accommodated. This constraint can be applied to queues, storages, buffers, and processing units. Models with finite capacity contrast with idealized infinite-capacity models and are used to reflect real-world resource limits, capacity planning, and performance trade-offs.

In queueing theory, a finite-capacity queue restricts the number of customers in the system to a maximum K. If the system already contains K customers, arriving customers are blocked or lost. The main performance measures include the blocking probability (the fraction of arrivals that find the system full), the effective arrival rate, the average number in the system, the average time in the system, and the utilization of the server. Classical examples include M/M/1/K and M/G/1/K.

Finite capacity is also central in inventory and production planning. Finite storage capacity forces decisions about ordering policies, production rates, and backordering. Capacity constraints can lead to lost sales or delayed fulfillment when demand exceeds available stock or when production capacity is saturated. In communications and computing, finite buffers and memory restrict the amount of data that can be held, affecting latency and packet loss.

Analysis techniques include Markov chains for memoryless service times, matrix-analytic methods for phase-type distributions, dynamic programming for optimization under capacity constraints, and discrete-event simulation. Applications span telecommunications, manufacturing, data centers, and logistics.