The M/M/1 queue is a basic model in queueing theory representing a single-server queue where arrivals follow a Poisson process, and service times are exponentially distributed. It is used to analyze systems with random arrival and service patterns, providing insights into metrics like average wait time and queue length.

M/M/1 Queue

M/M/1 queue

Queueing theory is a mathematical study of waiting lines or queues, which aims to predict queue lengths and waiting times in systems that involve processing tasks or servicing requests. It is widely used in operations research, telecommunications, and computer science to optimize resource allocation and improve service efficiency in various environments, from call centers to computer networks.

queueing theory

single-server queue

A Poisson process is a stochastic process that models the occurrence of events happening independently and at a constant average rate over time or space. It is widely used in fields such as telecommunications, finance, and natural sciences to describe random events like phone call arrivals, stock trades, or radioactive decay.

Poisson process

service times

exponentially distributed

random arrival

service patterns

average wait time

Queue length refers to the number of items or people waiting in line for service at any given time, and it is a critical metric for assessing the efficiency and performance of service systems. Understanding and managing queue length can help optimize resource allocation, reduce wait times, and improve customer satisfaction in various settings, from computer networks to retail environments.

Relevant Degrees

Your Lessons