A study of a loss system with priorities

Area of Science:

• Operations Research
• Applied Probability
• Telecommunications Engineering

Background:

• The Erlang B formula, a century-old model, calculates blocking probability in finite server loss systems.
• Applications range from telephony to healthcare resource management.
• Prioritization is crucial in modern service systems, necessitating extensions to the Erlang B formula.

Purpose of the Study:

• To analytically establish consistency between global balance equations and traffic loss arguments for preemptive priority loss systems.
• To derive known results for preemptive priority systems directly from global balance equations.
• To investigate the insensitivity property of the Erlang loss system in the context of preemptive priorities.

Main Methods:

• Formulation of a multidimensional Markov chain for the loss system with preemptive priorities.
• Derivation of steady-state probabilities using global balance equations.
• Analytical comparison with existing traffic loss arguments.
• Simulation-based analysis of blocking probabilities and service time distribution sensitivity.

Main Results:

• The study analytically confirms the consistency between global balance equations and traffic loss arguments for preemptive priority systems.
• A novel derivation of known results from global balance equations using Markov chain analysis is presented.
• Blocking probabilities for lower priority customers are shown to be sensitive to service time distributions, unlike the highest priority class.

Conclusions:

• The research provides a rigorous analytical foundation for preemptive priority loss systems.
• The insensitivity property of the Erlang loss system does not fully extend to preemptive priority systems.
• Service time variance significantly impacts blocking probabilities for lower priority traffic, offering insights for system optimization.