The Impact of Queue Length Information on Buffer Overflow in Parallel Queues

We consider a system consisting of N parallel queues, served by one server. Time is slotted, and the server serves one of the queues in each time slot, according to some scheduling policy. We first characterize the exponent of the buffer overflow probability and the most likely overflow trajectories under the Longest Queue First (LQF) scheduling policy. Under statistically identical arrivals to each queue, we show that the buffer overflow exponents can be simply expressed in terms of the total system occupancy exponent of $m$ parallel queues, for some m ≤ N. We next turn our attention to the rate of queue length information needed to operate a scheduling policy, and its relationship to the buffer overflow exponents. It is known that queue length blind policies such as processor sharing and random scheduling perform worse than the queue aware LQF policy, when it comes to buffer overflow probability. However, we show that the overflow exponent of the LQF policy can be preserved with arbitrarily infrequent queue length updates.National Science Foundation (U.S.) (Grant CNS-0626781)National Science Foundation (U.S.) (Grant CNS0915988)United States. Army Research Office. Multidisciplinary University Research Initiativ

Throughput Optimal Scheduling Over Time-Varying Channels in the Presence of Heavy-Tailed Traffic

We study the problem of scheduling over time varying links in a network that serves both heavy-tailed and light tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives heavy-tailed traffic (the heavy queue), and the other receives light-tailed traffic (the light queue). The queues are connected to the server through time-varying ON/OFF links, which model fading wireless channels. We first show that the policy that gives complete priority to the light-tailed traffic guarantees the best possible tail behavior of both queue backlog distributions, whenever the queues are stable. However, the priority policy is not throughput maximizing, and can cause undesirable instability effects in the heavy queue. Next, we study the class of throughput optimal max-weight-α scheduling policies. We discover a threshold phenomenon, and show that the steady state light queue backlog distribution is heavy-tailed for arrival rates above a threshold value, and light-tailed otherwise. We also obtain the exact tail coefficient of the light queue backlog distribution under max-weight-α scheduling. Finally, we study a log-max-weight scheduling policy, which is throughput optimal, and ensures that the light queue backlog distribution is light-tailed.National Science Foundation (U.S.) (Grant CNS-1217048)National Science Foundation (U.S.) (Grant CNS-0915988)National Science Foundation (U.S.) (CMMI-1234062)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-08-1-0238

A Framework for Scheduling Real-Time Traffic Over Wireless Channels

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryUSARO / W911NF-08-1-0238 and W-911-NF-0710287NSF / ECCS-0701604, CNS-07-21992, CNS-06-26584, and CSN-05-1953

Content-aware Caching and Traffic Management in Content Distribution Networks

The rapid increase of content delivery over the Internet has lead to the proliferation of content distribution networks (CDNs). Management of CDNs requires algorithms for request routing, content placement, and eviction in such a way that user delays are small. Our objective in this work is to design feasible algorithms that solve this trio of problems. We abstract the system of front-end source nodes and back-end caches of the CDN in the likeness of the input and output nodes of a switch. In this model, queues of requests for different pieces of content build up at the source nodes, which route these requests to a cache that contains the content. For each request that is routed to a cache, a corresponding data file is transmitted back to the source across links of finite capacity. Caches are of finite size, and the content of the caches can be refreshed periodically. A requested but missing item is fetched to the cache from the media vault of the CDN. In case of a lack of adequate space at the cache, an existing, unrequested item may be evicted from the cache in order to accommodate a new item. Every such cache refresh or media vault access incurs a finite cost. Hence the refresh periodicity allowed to the system represents our system cost. In order to obtain small user delays, our algorithms must consider the lengths of the request queues that build up at the nodes. Stable policies ensure the finiteness of the request queues, while good polices also lead to short queue lengths. We first design a throughput-optimal algorithm that solves the routing-placement eviction problem using instantaneous system state information. The design yields insight into the impact of different cache refresh and eviction policies on queue length. We use this and construct throughput optimal algorithms that engender short queue lengths. We then propose a regime of algorithms which remedies the inherent problem of wastage of capacity. We also develop heuristic variants, and we study their performance. We illustrate the potential of our approach and validate all our claims and results through simulations on different CDN topologies