M𝐚𝐫𝐤𝐨𝐯𝐢𝐚𝐧 𝐌/𝐌/𝟏 𝐐𝐮𝐞𝐮𝐞 𝐰𝐢𝐭𝐡 𝐃𝐨𝐮𝐛𝐥𝐞 𝐎𝐫𝐛𝐢𝐭 𝐑𝐞𝐭𝐫𝐢𝐚𝐥 U𝐧𝐝𝐞𝐫 𝐍−𝐏𝐨𝐥𝐢𝐜𝐲.

Abstract

In this work, we study Markovian M/M/1 queue with double orbit retrial under the service control policy i.e., N-policy. Upon arriving customers (premium/ordinary) who observe that the server is busy then he/she join the retrial orbit to try again their service. A ordinary customer wait in the ordinary orbit without any paid, whereas the premium customer wait in the premium orbit with paid some amount of money for receive good facility. Moreover, N policy states that the server is turned on only when there are N customers presents in the system. We use probability generating function for obtain the valuable performance indices such as expected queue length, expected system length, throughput, expected waiting time, etc.