On capital allocation for stochastic arrangement increasing actuarial risks

This paper studies the increasing convex ordering of the optimal discounted capital allocations for stochastic arrangement increasing risks with stochastic arrangement decreasing occurrence times. The application to optimal allocation of policy limits is presented as an illustration as well.

A Globally Gated Polling System with a Dormant Server

We study a globally gated polling system with a dormant server, which makes a halt at its home base when there are no customers present in the system. We derive an explicit expression for the cycle time distribution as well as for the waiting-time distribution at each of the queues. As a justification of the dormant server policy, we show the waiting time at each of the queues to be smaller (in the increasing-convex-ordering sense) than in the ordinary nondormant server case.

On an elementary characterization of the increasing convex ordering, by an application

In this short note, we present a simple characterization of the increasing convex ordering on the set of probability distributions on ℝ. We show its usefulness by providing a very short proof of a comparison result for M/GI/1 queues due to Daley and Rolski, and obtained by completely different means.

On an elementary characterization of the increasing convex ordering, by an application

In this short note, we present a simple characterization of the increasing convex ordering on the set of probability distributions on ℝ. We show its usefulness by providing a very short proof of a comparison result for M/GI/1 queues due to Daley and Rolski, and obtained by completely different means.

Optimality of the round-robin routing policy

In this paper we consider the problem of routing customers to identical servers, each with its own infinite-capacity queue. Under the assumptions that (i) the service times form a sequence of independent and identically distributed random variables with increasing failure rate distribution and (ii) state information is not available, we establish that the round-robin policy minimizes, in the sense of a separable increasing convex ordering, the customer response times and the numbers of customers in the queues.

Optimality of the round-robin routing policy

In this paper we consider the problem of routing customers to identical servers, each with its own infinite-capacity queue. Under the assumptions that (i) the service times form a sequence of independent and identically distributed random variables with increasing failure rate distribution and (ii) state information is not available, we establish that the round-robin policy minimizes, in the sense of a separable increasing convex ordering, the customer response times and the numbers of customers in the queues.