A Queueing Inventory System with Two Channels of Service

We consider a queueing inventory model with positive service time and two service channels. Channel I is a single server facility and channel II is a bulk service facility. There are two types of customers, type-I and type-II. The same type of commodity is served to both types of customers. Channel I provides service to type-I customers and channel II provides service to type-II customers. Service is initiated only if inventory is available. Bulk service is initiated at the end of a random clock or by the accumulation of N type-II customers. The inventory replenishment follows the $(s,S)$ policy with positive leadtime. The service time follows phase type distribution. Steady state analysis of the model is performed. Some performance measures are evaluated.