The Generalized Stochastic Knapsack
In this chapter we again consider a stochastic system consisting of C resource units and K classes of objects. And we again suppose that class-k objects have size bκ and arrive and depart at random times. But we now permit the arrival and service rates to depend on the current knapsack state. In particular, with n and S defined as in the previous chapter, the time until the next class-k arrival is exponentially distributed with parameter λ κ (n) when the knapsack is in state n. Analogously, the time until the next class-k departure is exponentially distributed with parameter μ κ (n) when the knapsack is in state n. Clearly, μ κ (n) must satisfy μ κ (n) = 0 whenever n κ = 0. Note that the generalized stochastic knapsack becomes the stochastic knapsack, as studied in the previous chapter, if we set λ κ (n) = λ κ and μ κ (n) = n κ μ κ for all n ∊ S.
KeywordsMigration Expense Convolution Lution Librium
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