Queueing Theory

Analyze and design service systems using queueing theory. Calculate expected waiting times, queue lengths, and server utilization for various queueing models to make capacity decisions.

Usage

Describe your service system to get queueing analysis, or ask about specific queueing models and their applications.

Examples

• "Calculate the average waiting time for an M/M/1 queue with arrival rate 5 and service rate 8"
• "How many servers do I need to keep average wait under 2 minutes?"
• "Explain Little's Law and how to apply it"

Guidelines

• Identify the arrival process, service process, and number of servers
• Use Little's Law (L = lambda * W) as a quick sanity check
• Utilization must be less than 1 for the system to be stable
• M/M/1 is the simplest model but often provides useful approximations
• Real systems often require simulation when analytical models are too simple