1,612 research outputs found
Join-Idle-Queue with Service Elasticity: Large-Scale Asymptotics of a Non-monotone System
We consider the model of a token-based joint auto-scaling and load balancing
strategy, proposed in a recent paper by Mukherjee, Dhara, Borst, and van
Leeuwaarden (SIGMETRICS '17, arXiv:1703.08373), which offers an efficient
scalable implementation and yet achieves asymptotically optimal steady-state
delay performance and energy consumption as the number of servers .
In the above work, the asymptotic results are obtained under the assumption
that the queues have fixed-size finite buffers, and therefore the fundamental
question of stability of the proposed scheme with infinite buffers was left
open. In this paper, we address this fundamental stability question. The system
stability under the usual subcritical load assumption is not automatic.
Moreover, the stability may not even hold for all . The key challenge stems
from the fact that the process lacks monotonicity, which has been the powerful
primary tool for establishing stability in load balancing models. We develop a
novel method to prove that the subcritically loaded system is stable for large
enough , and establish convergence of steady-state distributions to the
optimal one, as . The method goes beyond the state of the art
techniques -- it uses an induction-based idea and a "weak monotonicity"
property of the model; this technique is of independent interest and may have
broader applicability.Comment: 30 page
Dynamic Product Assembly and Inventory Control for Maximum Profit
We consider a manufacturing plant that purchases raw materials for product
assembly and then sells the final products to customers. There are M types of
raw materials and K types of products, and each product uses a certain subset
of raw materials for assembly. The plant operates in slotted time, and every
slot it makes decisions about re-stocking materials and pricing the existing
products in reaction to (possibly time-varying) material costs and consumer
demands. We develop a dynamic purchasing and pricing policy that yields time
average profit within epsilon of optimality, for any given epsilon>0, with a
worst case storage buffer requirement that is O(1/epsilon). The policy can be
implemented easily for large M, K, yields fast convergence times, and is robust
to non-ergodic system dynamics.Comment: 32 page
Breaking the Barrier Of 2 for the Competitiveness of Longest Queue Drop
We consider the problem of managing the buffer of a shared-memory switch that transmits packets of unit value. A shared-memory switch consists of an input port, a number of output ports, and a buffer with a specific capacity. In each time step, an arbitrary number of packets arrive at the input port, each packet designated for one output port. Each packet is added to the queue of the respective output port. If the total number of packets exceeds the capacity of the buffer, some packets have to be irrevocably rejected. At the end of each time step, each output port transmits a packet in its queue and the goal is to maximize the number of transmitted packets.
The Longest Queue Drop (LQD) online algorithm accepts any arriving packet to the buffer. However, if this results in the buffer exceeding its memory capacity, then LQD drops a packet from the back of whichever queue is currently the longest, breaking ties arbitrarily. The LQD algorithm was first introduced in 1991, and is known to be 2-competitive since 2001. Although LQD remains the best known online algorithm for the problem and is of practical interest, determining its true competitiveness is a long-standing open problem. We show that LQD is 1.707-competitive, establishing the first (2-?) upper bound for the competitive ratio of LQD, for a constant ? > 0
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