Читать книгу Queueing Theory 1 - Nikolaos Limnios - Страница 22

We consider the case where the service times are independent and the interarrival times depend on the distribution of the service times, and not just one parameter such as the mean:

 – let the service time, S, be of a general renewal type in discrete time with finite support. Let Let us write s = [s1, s2, ∙∙∙ , sM];

 – let there be K interarrival times with the selection of the interarrival time depending on the service time. Let be the interarrival time between the nth and the st customer if the kth interarrival is selected. Let

 – by the results in Alfa (2004), we can represent each of the K interarrival times by discrete PH distribution and in this case chose the remaining time approach. Let (α(k), T(k)) be the PH representation for the kth interarrival time distribution of dimension .

Next we define some parameters that will be used to relate the interarrival times to the service times.