Queuing Theory M/M/m Single Queue Multiple Servers

Queuing theory is a mathematical tool used to study waiting times and server idle times in service systems. The M/M/m model represents a single-queue, multiple-server queuing system typically applied to scenarios where multiple servers have identical service rates. Programmatic simulation serves as a common methodology for investigating queuing problems, utilizing computer algorithms to emulate service system operations and generate data on key performance indicators such as waiting times and server utilization rates. In practical implementation, this involves creating discrete-event simulation algorithms that track customer arrivals (following Poisson distribution), service times (exponentially distributed), and queue management logic. Key functions would include event scheduling, queue state monitoring, and statistical collection modules. Furthermore, queuing theory enables the analysis of how different service strategies impact waiting times and server utilization, along with optimization techniques for enhancing overall system performance through parameter tuning and resource allocation algorithms.