31、M/M1 + M2/1/N/K - Policy Queues: Monitoring Waiting Times and Performance Analysis

M/M1 + M2/1/N/K - Policy Queues: Monitoring Waiting Times and Performance Analysis

1. Introduction to Queueing Systems and Performance Monitoring

In the realm of queueing theory, the Poisson queueing systems are of great significance. By formulating an embedded Markov chain, we can study the M/M1 + M2/1/N/K - policy queues to monitor waiting times. This queueing model finds applications in various fields such as communications, networking, ATMs, and hospital systems.

1.1 Key Concepts and Calculations

• Calculating Queue Length and Waiting Time : We first find the distribution (q_j) using balance equations. Once (q_j) is determined, we can calculate the expected queue length (E(Q)) using the formula (E(Q)=\sum_{j = 0}