M/G/1 queue with regular and optional phases of services and vacations

Key Points

• This research aims to analyze a non-Markovian M/G/1 queue with phase type service and vacation times.
• Developed a mathematical framework for the queue system.
• Obtained the probability generating function for customer counts.
• Derived important performance measures in steady state.
• Provided numerical illustrations to support findings.
• The probability generating function informs about customer numbers during service and at departures.
• Various key performance measures are derived, enhancing queue evaluations.
• Numerical examples demonstrate practical applications of the findings.