Analysis of Queuing System Consisting of Multiple Parallel Channels in Series Connected to Non-Serial Servers with Finite Waiting Space and Balking, Reneging

Abstract

This chapter provides the steady-state analysis of more general queuing system in the sense that

• M service channels in series are linked with N non-serial channels having reneging and balking phenomenon where each of M service channels has identical multiple parallel channels.
• The input process is Poisson and the service time distribution is exponential.
• The service discipline follows SIRO-rule (Service in random order) instead of FIFO-rule (first in first out).
• The customer becomes impatient in queue after sometime and may leave the system without getting service.
• The input process depends upon the queue size in non-serial channels.
• Waiting space is finite.

The practical situations where such a model finds application are of common occurrence. For example, consider the administration of a particular state at the level of district head quarter consisting of Patwaris, Kanoongoes, Tehsildars, Sub-divisional magistrates, district commisioner etc. These officers correspond to the servers of serial channels. Education department, Health department, Irritation department etc. connected with the last server of serial queue correspond to non-serial channels. The people meet the officers of the district in connection with their problems.  It is also a common practice that the officers call the people for hearing randomly .Further District commisioner may send the customers to different departments such as education, health, irrigation etc. if their problems are related to such departments.