Two-commodity queueing-inventory system with phase-type distribution of service times
Özet
A two-commodity queueing-inventory system with phase-type service times and exponential
lead times is considered. There are two types of customers; Type 1 and Type 2. Demands
from each customer type occur independently according to a Poisson process with different
rates whereas the service times follow a phase-type distribution. Type 1 customers have a
non-preemptive priority over Type 2 customers. We assume a finite waiting space for Type
1 customers whereas there is no limit on the waiting room for Type 2 customers. Type i
customers demand only commodity i, i = 1, 2. For the ith commodity, Si and si represent,
respectively, the maximum inventory level and the reorder level. Whenever the inventory
level of ith commodity drops to si , an order is placed from retailer-i to make the inventory
level Si . The lead times of the commodities are exponentially distributed with different
parameters. When there is a Type i customer waiting in the queue, if the inventory level of
ith commodity is zero (or reaches zero), a decision of immediate purchase is made so as not
to lose the waiting customer. The queueing-inventory model in the steady-state is analyzed
using the matrix-geometric method. The system performance is examined for different values
of parameters. Besides, an optimization study is performed for some system parameters.
