A Simple Proof of the Optimality of a Threshold Policy in a Two-Server Queueing System
نویسنده
چکیده
Lin & Kumar [2] introduced a control model with a single queue and two heterogeneous servers. They showed, using policy iteration, that the slower server should only be used if the queue length is above a certain level, i.e., the optimal policy is of threshold type. In this note we give a simple iterative proof of this result. AMS Subject Classification (1991): 90B22, 90C40
منابع مشابه
Multiple vacation policy for MX/Hk/1 queue with un-reliable server
This paper studies the operating characteristics of an MX/Hk/1 queueing system under multiple vacation policy. It is assumed that the server goes for vacation as soon as the system becomes empty. When he returns from a vacation and there is one or more customers waiting in the queue, he serves these customers until the system becomes empty again, otherwise goes for another vacation. The brea...
متن کاملA Constrained Optimization Problem for a Two-Class Queueing Model
We discuss dynamic server control in a two-class service system under a constraint on the number of high-priority customers. A class of randomized threshold policies is defined, and is proven to contain an optimal policy in the case without abandonments. The proof of optimality is then used to construct heuristic policies for the case of low-priority abandonments, which we test numerically. The...
متن کاملVacation model for Markov machine repair problem with two heterogeneous unreliable servers and threshold recovery
Markov model of multi-component machining system comprising two unreliable heterogeneous servers and mixed type of standby support has been studied. The repair job of broken down machines is done on the basis of bi-level threshold policy for the activation of the servers. The server returns back to render repair job when the pre-specified workload of failed machines is build up. The first (seco...
متن کاملDiscrete Time Analysis of Multi-Server Queueing System with Multiple Working Vacations and Reneging of Customers
This paper analyzes a discrete-time $Geo/Geo/c$ queueing system with multiple working vacations and reneging in which customers arrive according to a geometric process. As soon as the system gets empty, the servers go to a working vacations all together. The service times during regular busy period, working vacation period and vacation times are assumed to be geometrically distributed. Customer...
متن کاملPartial-Fraction Decomposition Approach to the M/H2/2 Queue
Here, a two server queueing system with Poisson arrivals and two different types of customers (M/H2/2 queue) is analyzed. A novel straightforward method is presented to acquire the exact and explicit forms of the performance measures. First, the steady state equations along with their Z-transforms are derived for the aforementioned queueing system. Using some limiting behaviors of the steady-st...
متن کامل