Abstract：The partial working vacations policy was considered based on conventional M/M/c queue.
During the vacation period, some of servers do not entirely stop service, and service the new
customers at a lower service rate, while the other servers stop service with a normal vacation.
With the consideration of negative customers, Npolicy is introduced as vacation stopping
policy. The negative customers only remove positive customers who are being served at the head of
the queue one by one. When there is no positive customer in the system, the arrived negative
customers will disappear automatically without service. At the end of a vacation, if the customer
numbers in system are not less than N, the system will stop vacation. Otherwise, the system
continues to have vacation. Based on quasi birth and death process and matrix geometric solution,
the steady state distribution of queue length was obtained. The conditional stochastic
decomposition was established for all busy servers.
2013, Vol. 34 
