Discrete- Time Queueing Model 𝐺𝑒𝑜𝑋/𝐺/∞ with Bulk Arrival Rule
Pukazhenthi. N1, Ramki. S2
1Pukazhenthi. N*, Assistant professor, Department of statistics, Annamalai University, chidambarm, Tamilnadu,
2Ramki. S, Research scholar, Department of statistics, Annamalai University, Chidambaram, Tamilnadu.
Manuscript received on January 26, 2020. | Revised Manuscript received on February 05, 2020. | Manuscript published on February 30, 2020. | PP: 2585-2589 | Volume-9 Issue-3, February 2020. | Retrieval Number: C5592029320/2020©BEIESP | DOI: 10.35940/ijeat.C5592.029320
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Abstract: A discrete time queueing model 𝑮𝒆𝒐𝑿/𝑮/∞ is considered to estimate of the number of customers in the system. The arrivals, which are in groups of size X, inter-arrivals times and service times are distributed independent. The inter-arrivals fallows geometric distribution with parameter p and service times follows general distribution with parameter µ, we have derive the various transient state solution along with their moments and numerical illustrations in this paper.
Keywords: Discrete time, Customers, Group size, Inter-arrival, Transient distributions, Geometric distribution.