System Objectives Clause Samples

System Objectives. In this paper we consider the response of a firm to alternate contracts, and so the system objectives of the firm depend on the form of these contracts and the firm’s objective with respect to non-contract customers. Suppose that contract customers are guaranteed a minimum average performance on some measure of delay. Let Π be the set of all Head-of-Line policies. Let gπ(W1) be the random variable of interest for a given policy π ∈ Π. For example, under a delay percentile contract, for a given policy π, gπ(W1) = IW1 ≤D and the contract requires E[gπ(W1)] ≥ γ. Non-contract customers have no guarantees on delay. As discussed in the introduction, the firm wishes to give them good delay performance in order to increase the chance that they repeat their business or even convert to contract customers. We do not explicitly model either of these motivations, and instead assume we seek to minimize the average of some measure of the non-contract customers’ delay, hπ(W2). Such was the approach of the call center that served as a motivation for this research. For simplicity, throughout the paper we assume that hπ(W2) = W2. The problem we consider is: min E[hπ(W2)] s.t. E[gπ(W1)] K, π∈Π for some constant K. As discussed earlier, in order to approach this problem, we consider an appropriately scaled ▇▇▇▇▇▇ version of the problem in heavy traffic. Also as noted earlier, the form of both the objective and constraint differs from those traditionally used in the heavy-traffic literature because they consider averages. For these reasons we consider asymptotic optimality among policies and sequences of scaled systems that: 1. Have an (α, β) impulse-exponential heavy-traffic limit; 2. Exhibit state-space collapse; and 3. Exhibit steady-state convergence. While such as definition of asymptotic optimality is in some sense more restrictive than those in earlier heavy-traffic work because it carries with it a number of assumptions it is also more general because it provides results for system averages. In order to define the limiting problem, let gˆπ (·) and hˆπ () be appropriately scaled functions of interest such that: gˆπ (W˜ n∗ ) = gπ(Wn∗ ), hˆπ (W˜ n∗ ) = hπ(Wn∗ ), and