1,288 research outputs found
Career: fundamental lower bound and tradeoff problems in networking
Issued as final reportNational Science Foundation (U.S.
On service guarantees of fair-queueing schedulers in real systems
Abstract In most systems, fair-queueing packet schedulers are the algorithms of choice for providing bandwidth and delay guarantees. These guarantees are computed assuming that the scheduler is directly attached to the transmit unit with no interposed buffering, and, for timestamp-based schedulers, that the exact number of bits transmitted is known when timestamps need to be updated. Unfortunately, both assumptions are unrealistic. In particular, real communication devices normally include FIFO queues (possibly very deep ones) between the scheduler and the transmit unit. And the presence of these queues does invalidate the proofs of the service guarantees of existing timestamp-based fair-queueing schedulers. In this paper we address these issues with the following two contributions. First, we show how to modify timestamp-based, worst-case optimal and quasi-optimal fair-queueing schedulers so as to comply with the presence of FIFO\queues, and with uncertainty on the number of bits transmitted. Second, we provide analytical bounds of the actual guarantees provided, in these real-world conditions, both by modified timestamp-based fair-queueing schedulers and by basic round-robin schedulers. These results should help designers to make informed decisions and sound tradeoffs when building systems
QoS Routing with worst-case delay constraints: models, algorithms and performance analysis
In a network where weighted fair-queueing schedulers are used at each link, a flow is guaranteed an end-to-end worst-case delays which depends on the rate reserved for it at each link it traverses. Therefore, it is possible to compute resource-constrained paths that meet target delay constraints, and optimize some key performance metrics (e.g., minimize the overall reserved rate, maximize the remaining capacity at bottleneck links, etc.). Despite the large amount of literature that has appeared on weighted fair-queueing schedulers since the mid '90s, this has so far been done only for a single type of scheduler, probably because the complexity of solving the problem in general appeared forbidding. In this paper, we formulate and solve the optimal path computation and resource allocation problem for a broad category of weighted fair-queueing schedulers, from those emulating a Generalized Processor Sharing fluid server to variants of Deficit Round Robin. We classify schedulers according to their latency expressions, and show that a significant divide exists between those where routing a new flow affects the performance of existing flows, and those for which this do not happen. For the former, explicit admission control constraints are required to ensure that existing flows still meet their deadline afterwards. However, despite this major difference and the differences among categories of schedulers, the problem can always be formulated as a Mixed-Integer Second-Order Cone problem (MI-SOCP), and be solved at optimality in split-second times even in fairly large networks
Throughput and Delay Optimization of Linear Network Coding in Wireless Broadcast
Linear network coding (LNC) is able to achieve the optimal
throughput of packet-level wireless broadcast, where a sender
wishes to broadcast a set of data packets to a set of receivers
within its transmission range through lossy wireless links. But
the price is a large delay in the recovery of individual data
packets due to network decoding, which may undermine all the
benefits of LNC. However, packet decoding delay minimization and
its relation to throughput maximization have not been well
understood in the network coding literature.
Motivated by this fact, in this thesis we present a comprehensive
study on the joint optimization of throughput and average packet
decoding delay (APDD) for LNC in wireless broadcast. To this end,
we reveal the fundamental performance limits of LNC and study the
performance of three major classes of LNC techniques, including
instantly decodable network coding (IDNC), generation-based LNC,
and throughput-optimal LNC (including random linear network
coding (RLNC)).
Various approaches are taken to accomplish the study, including
1) deriving performance bounds, 2) establishing and modelling
optimization problems, 3) studying the hardness of the
optimization problems and their approximation, 4) developing new
optimal and heuristic techniques that take into account practical
concerns such as receiver feedback frequency and computational
complexity.
Key contributions of this thesis include:
- a necessary and sufficient condition for LNC to achieve the
optimal throughput of wireless broadcast;
- the NP-hardness of APDD minimization;
- lower bounds of the expected APDD of LNC under random packet
erasures;
- the APDD-approximation ratio of throughput-optimal LNC, which
has a value of between 4/3 and 2. In particular, the ratio of
RLNC is exactly 2;
- a novel throughput-optimal, APDD-approximation, and
implementation-friendly LNC technique;
- an optimal implementation of strict IDNC that is robust to
packet erasures;
- a novel generation-based LNC technique that generalizes some of
the existing LNC techniques and enables tunable throughput-delay
tradeoffs
Delay-constrained Routing Problems: Accurate Scheduling Models and Admission Control
As shown in [1], the problem of routing a flow subject to a worst-case end-to-end delay constraint
in a packed-based network can be formulated as a Mixed-Integer Second-Order Cone Program,
and solved with general-purpose tools in real time on realistic instances. However, that result only
holds for one particular class of packet schedulers, Strictly Rate-Proportional ones, and implicitly
considering each link to be fully loaded, so that the reserved rate of a flow coincides with its
guaranteed rate. These assumptions make latency expressions simpler, and enforce perfect isolation
between flows, i.e., admitting a new flow cannot increase the delay of existing ones. Other
commonplace schedulers both yield more complex latency formulæ and do not enforce flow isolation.
Furthermore, the delay actually depends on the guaranteed rate of the flow, which can be
significantly larger than the reserved rate if the network is unloaded. In this paper we extend the
result to other classes of schedulers and to a more accurate representation of the latency, showing
that, even when admission control needs to be factored in, the problem is still efficiently solvable
for realistic instances, provided that the right modeling choices are made.
Keywords: Routing problems, maximum delay constraints, scheduling algorithms, admission
control, Second-Order Cone Programs, Perspective Reformulatio
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