Queueing Inventory System in Transport Problem

Abstract

In this paper, we consider the batch arrival of customers to a transport station. Customers belonging to each category is considered as a single entity according to a BMMAP. An Erlang clock of order m starts ticking when the transport vessel reaches the station. When the Lth stage of the clock is reached, an order for the next vessel is placed. The lead time for arrival of the vessel follows exponential distribution. There are two types of rooms in this system: the waiting rooms and the service rooms for customers in the transport station and in the vessel, respectively. The waiting room capacity for customers of type 1 is infinite whereas those for customer of type 2,…,k are of finite capacities. The service room capacity Cj for customer type j,j=1,2,…,k is finite. Upon arrival, customers of category j occupy seats designated for that category in the vessel, provided there is at least one vacancy belonging to that category. The total number of vessels with the operator is h*. The service time of each vessel follows exponential distribution with parameter μ. Each group of customers belong to category j searches independently for customers of this category to mobilize passengers when the Erlang clock reaches L1 where L1L. The search time for customers of category j follows exponential distribution with parameter λj. The stability condition is derived. Some performance measures are estimated.

Keywords

• batch marked markovian arrival process
• batch arrival
• Erlang clock
• batch service
• matrix analytic method