STATIONARY CHARACTERISTICS OF UNRELIABLE QUEUEING SYSTEM WITH BATCH MARKOVIAN ARRIVAL PROCESS AND RESERVE SERVER

• Main Author: V. I. Klimenok
• Format: Article
• Language: Russian
• Published: The United Institute of Informatics Problems of the National Academy of Sciences of Belarus 2016-10-01
• Series: Informatika
• Online Access: https://inf.grid.by/jour/article/view/83

In the paper, a queueing system with unreliable server and so called «cold» redundancy is analyzed. The system consists of an infinite buffer, the main unreliable server and the reliable reserve server. The term «cold reserve» means that the reserve server is off until the main server is in good order and is activated when the main server is under repair. The input flow to the system is a BMAP (Batch Markovian Arrival Process). Breakdowns arrive to the main server according to a MAP (Markovian Arrival Process). Service times as well as repair time have PH (Phase type) distribution. A condition for the stable operation of the system is shown, its stationary distribution and the main characteristics are calculated and the expression for the Laplace – Stieltjes transform of the sojourn time distribution is derrived.