We give a branch-and-cut algorithm for solving linear programs (LPs) with continuous separable piecewise-linear cost functions (PLFs). Models for PLFs use continuous variables in special-ordered sets of type 2 (SOS2). Traditionally, SOS2 constraints are enforced by introducing auxiliary binary variables and other linear constraints on them. Alternatively, we can enforce SOS2 constraints by branching on them, thus dispensing with auxiliary binary variables. We explore this approach further by studying the inequality description of the convex hull of the feasible set of LPs with PLFs in the space of the continuous variables, and using the new cuts in a branch-and-cut scheme without auxiliary binary variables. We give two families of valid inequalities. The first family is obtained by lifting the convexity constraints. The second family consists of lifted cover inequalities. Finally, we report computational results that demonstrate the effectiveness of our cuts, and that branch-and-cut without auxiliary binary variables is significantly more practical than the traditional mixed-integer programming approach.
͑Doc. ID 68980͒ We explore the problem of bandwidth management for the evolutionary upgrade of WDM EPONs. We divide the bandwidth management problem into two subproblems: (1) grant sizing and (2) grant scheduling. We then apply a scheduling theoretical approach to find a best scheduler for WDM EPONs. We show by means of extensive simulations that a multidimensional scheduling approach using results from scheduling theory can provide much better bandwidth management by means of better wavelength utilization than a static wavelength assignment. We also show that an online scheduling approach can provide lower queueing delays than a cyclical offline scheduling approach. We conclude with some specific guidance on future research on bandwidth management for WDM EPONs.
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