A unified approach to gi/m(n)/l/k and m(n)/g/1/k queues via finite quasi-birth-death processes

Abstract

In this paper, we provide a unified approach to study GI/M/LK Queses with state-dependent services and M/G/1/K Queueswith state dependent arrivals First,we describe such queses in term of finite quasi-birth-death (QBD) arrivalS. First, describe wen this paper, we treat GI/M/l/K queues with state-dependent services and M/G/l/K queues with state-dependent arrivals. First,we describe such queues in term of finite quasi-birth-death (QBD) processes by approximating the general distribution on term of phase-type distributions. Then by solving the corresponding Matrix equation for the QBD

processes and by showing that the results obtained are free from the representation we drive various existing results together with

some new result for important characteistics in queuesing systems.

Keywords:

• Finite queue,
• Finite quasi-birth-death process,
• Phase-type distribution,
• Queue-length,
• Busy period,
• Virtual waiting time