Teoría de colas. Modelo M/M/s

Abstract

[en] In this Final Degree Project, the Queuing Theory is developed around its best known model: the M/M/s. To do this, two previous theory sections necessary for this model are presented. The first of these sections is about the Poisson process, where definitions and results on the exponential distribution are included and then the Poisson process itself is presented. The Poisson process helps us determine the distribution of customer arrivals in M/M/s queuing systems. The second of these sections is about continuous time Markov chains. This section plays a central role in M/M/s queuing systems, since these are a particular case of birth and death processes, which are nothing more than a specific type of continuous-time Markov chain. With this, section number 4 focuses on the development of M/M/s queuing systems with the objective of knowing measures of effectiveness in relation to these queues and knowing the most appropriate number of servers for a M/M/s queue. To this end, birth and death processes, the concept of stationary distribution and Little’s formulas are introduced earlier. To give practical sense to the theoretical abstraction, in section number 6 a real case of application of the M/M/s model is presented, before presenting in section number 5 the basic theory of queuing networks.