Stability of a Queuing System with Concurrent Service and Locking

Resource sharing systems, such as database management systems, utilize various types of locking to maintain consistency. Most locking mechanisms cause some resources to remain idle at certain times when there is work for them to do, inducing a decrease in the system's capacity. This decrease of capacity is reflected in the stability condition for the locking system as compared to the system without locking. We consider the following locking system. There are N servers operating in parallel and two types of incoming customers. The first type corresponds to simple customers, i.e., customers with no locking requirements, and the second corresponds to customers that have to be processed simultneously by all N servers.