非指數服務型態及符記佇列

Abstract

我們考慮的模型是由兩個串聯的服務站所構成的服務系統，其中每個服務站各有一個服務者。假設這兩個服務站的服務時間分配函數如下：前者具有有限的混合艾倫分配，而後者為一般分配。由系統外進入之顧客人數服從卜瓦松分配，且須經由一符記佇列中取得一符記始得進入系統內，否則將被拒絕而離開此系統。當一顧客完成全部服務後便立即將所擁有之符記還回此佇列。我們假設佇列數目固定，以控制系統內之人數。在此論文中，我們將導出一個由外進入之顧客發現佇列中沒有符記的機率，以及對於同一個符記其循環所花時間的拉普拉氏─司提吉轉換。

We consider a simple two-station series, single-server (at each station) queuing model with external arrivals according to a poisson process. And assuming one is general server and the other one whose service time distribution is a finite mixture of Eriang distribution. Furthermore, the customers should get `a token from the token queue to enter the system. We will construct an embedded Markov chain of this model and study the ergodicity of the chain at the departure points, then use it to derive a formula of the loss probability i.e., the probability of an arriving customer find no token in the token queue. Finally, we give the Laplace-Stieltjes transform of the cycle time for a token i.e., the time between successive departure for a token to the server 2.