17,136 research outputs found
Delay versus Stickiness Violation Trade-offs for Load Balancing in Large-Scale Data Centers
Most load balancing techniques implemented in current data centers tend to
rely on a mapping from packets to server IP addresses through a hash value
calculated from the flow five-tuple. The hash calculation allows extremely fast
packet forwarding and provides flow `stickiness', meaning that all packets
belonging to the same flow get dispatched to the same server. Unfortunately,
such static hashing may not yield an optimal degree of load balancing, e.g.,
due to variations in server processing speeds or traffic patterns. On the other
hand, dynamic schemes, such as the Join-the-Shortest-Queue (JSQ) scheme,
provide a natural way to mitigate load imbalances, but at the expense of
stickiness violation.
In the present paper we examine the fundamental trade-off between stickiness
violation and packet-level latency performance in large-scale data centers. We
establish that stringent flow stickiness carries a significant performance
penalty in terms of packet-level delay. Moreover, relaxing the stickiness
requirement by a minuscule amount is highly effective in clipping the tail of
the latency distribution. We further propose a bin-based load balancing scheme
that achieves a good balance among scalability, stickiness violation and
packet-level delay performance. Extensive simulation experiments corroborate
the analytical results and validate the effectiveness of the bin-based load
balancing scheme
A phase-field model for cohesive fracture
In this paper, a phase-field model for cohesive fracture is developed. After casting the cohesive zone approach in an energetic framework, which is suitable for incorporation in phase-field approaches, the phase-field approach to brittle fracture is recapitulated. The approximation to the Dirac function is discussed with particular emphasis on the Dirichlet boundary conditions that arise in the phase-field approximation. The accuracy of the discretisation of the phase field, including the sensitivity to the parameter that balances the field and the boundary contributions, is assessed at the hand of a simple example. The relation to gradient-enhanced damage models is highlighted, and some comments on the similarities and the differences between phase-field approaches to fracture and gradient-damage models are made. A phase-field representation for cohesive fracture is elaborated, starting from the aforementioned energetic framework. The strong as well as the weak formats are presented, the latter being the starting point for the ensuing finite element discretisation, which involves three fields: the displacement field, an auxiliary field that represents the jump in the displacement across the crack, and the phase field. Compared to phase-field approaches for brittle fracture, the modelling of the jump of the displacement across the crack is a complication, and the current work provides evidence that an additional constraint has to be provided in the sense that the auxiliary field must be constant in the direction orthogonal to the crack. The sensitivity of the results with respect to the numerical parameter needed to enforce this constraint is investigated, as well as how the results depend on the orders of the discretisation of the three fields. Finally, examples are given that demonstrate grid insensitivity for adhesive and for cohesive failure, the latter example being somewhat limited because only straight crack propagation is considered
A new blade element method for calculating the performance of high and intermediate solidity axial flow fans
A method is presented to design and predict the performance of axial flow rotors operating in a duct. The same method is suitable for the design of ducted fans and open propellers. The unified method is based on the blade element approach and the vortex theory for determining the three dimensional effects, so that two dimensional airfoil data can be used for determining the resultant force on each blade element. Resolution of this force in the thrust and torque planes and integration allows the total performance of the rotor, fan or propeller to be predicted. Three different methods of analysis, one based on a momentum flow theory; another on the vortex theory of propellers; and a third based on the theory of ducted fans, agree and reduce cascade airfoil data to single line as a function of the loading and induced angle of attack at values of constant inflow angle. The theory applies for any solidity from .01 to over 1 and any blade section camber. The effects of the duct and blade number can be determined so that the procedure applies over the entire range from two blade open propellers, to ducted helicopter tail rotors, to axial flow compressors with or without guide vanes, and to wind tunnel drive fans
Queue-Based Random-Access Algorithms: Fluid Limits and Stability Issues
We use fluid limits to explore the (in)stability properties of wireless
networks with queue-based random-access algorithms. Queue-based random-access
schemes are simple and inherently distributed in nature, yet provide the
capability to match the optimal throughput performance of centralized
scheduling mechanisms in a wide range of scenarios. Unfortunately, the type of
activation rules for which throughput optimality has been established, may
result in excessive queue lengths and delays. The use of more
aggressive/persistent access schemes can improve the delay performance, but
does not offer any universal maximum-stability guarantees. In order to gain
qualitative insight and investigate the (in)stability properties of more
aggressive/persistent activation rules, we examine fluid limits where the
dynamics are scaled in space and time. In some situations, the fluid limits
have smooth deterministic features and maximum stability is maintained, while
in other scenarios they exhibit random oscillatory characteristics, giving rise
to major technical challenges. In the latter regime, more aggressive access
schemes continue to provide maximum stability in some networks, but may cause
instability in others. Simulation experiments are conducted to illustrate and
validate the analytical results
Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows
We consider a fluid queue fed by multiple On-Off flows with heavy-tailed
(regularly varying) On periods. Under fairly mild assumptions, we prove that
the workload distribution is asymptotically equivalent to that in a reduced
system. The reduced system consists of a ``dominant'' subset of the flows, with
the original service rate subtracted by the mean rate of the other flows. We
describe how a dominant set may be determined from a simple knapsack
formulation. The dominant set consists of a ``minimally critical'' set of
On-Off flows with regularly varying On periods. In case the dominant set
contains just a single On-Off flow, the exact asymptotics for the reduced
system follow from known results. For the case of several
On-Off flows, we exploit a powerful intuitive argument to obtain the exact
asymptotics. Combined with the reduced-load equivalence, the results for the
reduced system provide a characterization of the tail of the workload
distribution for a wide range of traffic scenarios
Lingering Issues in Distributed Scheduling
Recent advances have resulted in queue-based algorithms for medium access
control which operate in a distributed fashion, and yet achieve the optimal
throughput performance of centralized scheduling algorithms. However,
fundamental performance bounds reveal that the "cautious" activation rules
involved in establishing throughput optimality tend to produce extremely large
delays, typically growing exponentially in 1/(1-r), with r the load of the
system, in contrast to the usual linear growth.
Motivated by that issue, we explore to what extent more "aggressive" schemes
can improve the delay performance. Our main finding is that aggressive
activation rules induce a lingering effect, where individual nodes retain
possession of a shared resource for excessive lengths of time even while a
majority of other nodes idle. Using central limit theorem type arguments, we
prove that the idleness induced by the lingering effect may cause the delays to
grow with 1/(1-r) at a quadratic rate. To the best of our knowledge, these are
the first mathematical results illuminating the lingering effect and
quantifying the performance impact.
In addition extensive simulation experiments are conducted to illustrate and
validate the various analytical results
Automatic Romaine Heart Harvester
The Romaine Robotics Senior Design Team developed a romaine lettuce heart trimming system in partnership with a Salinas farm to address a growing labor shortage in the agricultural industry that is resulting in crops rotting in the field before they could be harvested. An automated trimmer can alleviate the most time consuming step in the cut-trim-bag harvesting process, increasing the yields of robotic cutters or the speed of existing laborer teams. Leveraging the Partner Farm’s existing trimmer architecture, which consists of a laborer loading lettuce into sprungloaded grippers that are rotated through vision and cutting systems by an indexer, the team redesigned geometry to improve the loading, gripping, and ejection stages of the system. Physical testing, hand calculations, and FEA were performed to understand acceptable grip strengths and cup design, and several wooden mockups were built to explore a new actuating linkage design for the indexer. The team manufactured, assembled, and performed verification testing on a full-size metal motorized prototype that can be incorporated with the Partner Farm’s existing cutting and vision systems. The prototype met all of the established requirements, and the farm has implemented the redesign onto their trimmer. Future work would include designing and implementing vision and cutting systems for the team’s metal prototype
GPS queues with heterogeneous traffic classes
We consider a queue fed by a mixture of light-tailed and heavy-tailed traffic. The two traffic classes are served in accordance with the generalized processor sharing (GPS) discipline. GPS-based scheduling algorithms, such as weighted fair queueing (WFQ), have emerged as an important mechanism for achieving service differentiation in integrated networks. We derive the asymptotic workload behavior of the light-tailed class for the situation where its GPS weight is larger than its traffic intensity. The GPS mechanism ensures that the workload is bounded above by that in an isolated system with the light-tailed class served in isolation at a constant rate equal to its GPS weight. We show that the workload distribution is in fact asymptotically equivalent to that in the isolated system, multiplied with a certain pre-factor, which accounts for the interaction with the heavy-tailed class. Specifically, the pre-factor represents the probability that the heavy-tailed class is backlogged long enough for the light-tailed class to reach overflow. The results provide crucial qualitative insight in the typical overflow scenario
Delay Performance and Mixing Times in Random-Access Networks
We explore the achievable delay performance in wireless random-access
networks. While relatively simple and inherently distributed in nature,
suitably designed queue-based random-access schemes provide the striking
capability to match the optimal throughput performance of centralized
scheduling mechanisms in a wide range of scenarios. The specific type of
activation rules for which throughput optimality has been established, may
however yield excessive queues and delays.
Motivated by that issue, we examine whether the poor delay performance is
inherent to the basic operation of these schemes, or caused by the specific
kind of activation rules. We derive delay lower bounds for queue-based
activation rules, which offer fundamental insight in the cause of the excessive
delays. For fixed activation rates we obtain lower bounds indicating that
delays and mixing times can grow dramatically with the load in certain
topologies as well
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