The Queuing System With Working Vacation And Impatient Customers

Servi and Finn studied a new police of working vacation: during a vacation, theserver doesn’t completely stop working, but works at a lower rate. If a working vacationis over and the system does not have customers, the next working vacation will start. Itcalled multiple working vacations. On the other hand, the server begins a regular period.This called single working vacation. The queuing systems with working vacation, whichhas been widely in communications networks, computer systems, production managingand so on, are researched and discussed by many authors. Subsequently, impatient cus-tomers and the queuing systems with working vacation are introduced; many authorsalso put attention to this field at the same time.In this thesis, the queuing systems with working vacation and impatient customersare researched. On the basis of previous analysis, we further study the queuing systemswith working vacation and impatient customers. The content is organized as follow:1. An M/M/1queue system with the threshold of working vacation is studied. Itis a new police: when the numbers of customers achieve a certain value in the vacationperiod, the server can come back to the normal working level from the vacation. Other-wise, the server goes on working to the end of working vacation. We analyze the modeland obtain balance equations by the state transition, derive the queue length and waitingtime. Finally, several numerical results are presented.2. An M/M/1queue system with a single working vacation and impatient cus-tomers is researched. The server must wait until the first arrival if the server comes backto the system from a vacation and finds the system has not any customer, thereafter,opens a normal period. Otherwise, the server directly services. The customer goes awaythe system and doesn’t return, because the impatient time goes beyond. We derive thebalance equations for the system by the state transition and analyze the model, variousperformance measures are derived at last. Finally, several numerical examples are pre-sented to verify the results we get.