We study a variant of Naor’s [23] online packet buffering model: We are given a (non-preemptive) ... more We study a variant of Naor’s [23] online packet buffering model: We are given a (non-preemptive) fifo buffer (e.g., in a network switch or a router) and packets that request transmission arrive over time. Any packet has an intrinsic value R and we have to decide whether to accept or reject it. In each time-step, the first packet in the buffer
We analyze a natural greedy algorithm, GREEDY, which sends in each time step a packet with the gr... more We analyze a natural greedy algorithm, GREEDY, which sends in each time step a packet with the greatest value. For general packet values $(v_1 < \cdots < v_m)$, we show that GREEDY is $(1+r)$-competitive, where $r = \max_{1\le i \le m-1} \{v_i/v_{i+1}\}$. Furthermore, we show a lower bound of $2 - v_m / \sum_{i=1}^m v_i$ on the competitiveness of any deterministic online algorithm. In the special case of two packet values (1 and $\alpha > 1$), GREEDY is shown to be optimal with a competitive ratio of $(\alpha + 2)/(\alpha + 1)$.
A set of n independent jobs is to be scheduled without preemption on m identical parallel machine... more A set of n independent jobs is to be scheduled without preemption on m identical parallel machines. For each job j, a so called diffuse adversary chooses the distribution F j of the random processing time P j from a certain class of distributions \(\mathcal{F}_{j}\) . The scheduler is given the expectation \(\mu_{j}=\mathbb{E}[P_{j}]\) , but the actual duration is not known in advance. A positive weight w j is associated with each job j and all jobs are ready for execution at time zero. The objective is to minimise the expected competitive ratio max \(_{F\in f} \mathbb{E}[\frac{\Sigma_{j}\omega_{j}C_{j}}{OPT}]\) , where C j denotes the completion time of job j and OPT the offline optimum value. The scheduler determines a list of jobs, which is then scheduled in non-preemptive static list policy. We show a general bound on the expected competitive ratio for list scheduling algorithms, which holds for a class of so called new-better-than-used processing time distributions. This class includes, among others the exponential distribution. Our bound depends on the probability of any pair of jobs being in the wrong order in the list of an arbitrary list scheduling algorithm, compared to an optimum list. As a special case, we show that the so called WSEPT algorithm achieves \(\mathbb{E}[\frac{WSEPT}{OPT}]\leq 3-{\frac{1}{m}}\) for exponential distributed processing times.
We study a variant of Naor’s [23] online packet buffering model: We are given a (non-preemptive) ... more We study a variant of Naor’s [23] online packet buffering model: We are given a (non-preemptive) fifo buffer (e.g., in a network switch or a router) and packets that request transmission arrive over time. Any packet has an intrinsic value R and we have to decide whether to accept or reject it. In each time-step, the first packet in the buffer
We analyze a natural greedy algorithm, GREEDY, which sends in each time step a packet with the gr... more We analyze a natural greedy algorithm, GREEDY, which sends in each time step a packet with the greatest value. For general packet values $(v_1 < \cdots < v_m)$, we show that GREEDY is $(1+r)$-competitive, where $r = \max_{1\le i \le m-1} \{v_i/v_{i+1}\}$. Furthermore, we show a lower bound of $2 - v_m / \sum_{i=1}^m v_i$ on the competitiveness of any deterministic online algorithm. In the special case of two packet values (1 and $\alpha > 1$), GREEDY is shown to be optimal with a competitive ratio of $(\alpha + 2)/(\alpha + 1)$.
A set of n independent jobs is to be scheduled without preemption on m identical parallel machine... more A set of n independent jobs is to be scheduled without preemption on m identical parallel machines. For each job j, a so called diffuse adversary chooses the distribution F j of the random processing time P j from a certain class of distributions \(\mathcal{F}_{j}\) . The scheduler is given the expectation \(\mu_{j}=\mathbb{E}[P_{j}]\) , but the actual duration is not known in advance. A positive weight w j is associated with each job j and all jobs are ready for execution at time zero. The objective is to minimise the expected competitive ratio max \(_{F\in f} \mathbb{E}[\frac{\Sigma_{j}\omega_{j}C_{j}}{OPT}]\) , where C j denotes the completion time of job j and OPT the offline optimum value. The scheduler determines a list of jobs, which is then scheduled in non-preemptive static list policy. We show a general bound on the expected competitive ratio for list scheduling algorithms, which holds for a class of so called new-better-than-used processing time distributions. This class includes, among others the exponential distribution. Our bound depends on the probability of any pair of jobs being in the wrong order in the list of an arbitrary list scheduling algorithm, compared to an optimum list. As a special case, we show that the so called WSEPT algorithm achieves \(\mathbb{E}[\frac{WSEPT}{OPT}]\leq 3-{\frac{1}{m}}\) for exponential distributed processing times.
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