The one-dimensional on-line bin-packing problem is considered, A simple
O
(1)-space and
O
(
n
)-time algorithm, called HARMONIC
M
, is presented. It is shown that this algorithm can achieve a worst-case performance ratio of less than 1.692, which is better than that of the
O
(
n
)-space and
O
(
n
log
n
)-time algorithm FIRST FIT. Also shown is that 1.691 … is a lower bound for
all
0
(1)-space on-line bin-packing algorithms. Finally a revised version of HARMONIC
M
, an
O
(
n
)-space and
O
(
n
)- time algorithm, is presented and is shown to have a worst-case performance ratio of less than 1.636.
Packet scheduling is key to QoS capabilities of broadband wired and wireless networks. In a heterogeneous traffic environment, a comprehensive QoS packet scheduler must strike a balance between flow fairness and access delay. Many advanced packet scheduling solutions have targeted fair bandwidth allocation while protecting delay-constrained traffic by adding priority queue(s) on top of a fair bandwidth scheduler. Priority queues are known to cause performance uncertainties and thus various modifications have been proposed. In this paper, we present a packet queueing engine dubbed Fractional Service Buffer (FSB) which, when coupled with a configurable flow scheduler, can achieve desired QoS objectives such as fair throughputs and differentiated delay guarantees. The flow scheduler is a buffer-less module that can be configured to assign each incoming packet a delay class in accordance with its owner flow's QoS status. The FSB uses one buffer for each delay class and serves the buffers with a special queueing discipline that advances packets in lower-priority buffers to meet their classspecific delay guarantees. Key performance metrics such as delay limit and probability of delay limit violation are derived, as a function of key FSB parameters, for each delay class in the packet queueing engine using diffusion approximations. OPNET simulations verify these analytical results.
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