Properties of Probability Distributions with Monotone Hazard Rate

Barlow, Richard E.; Marshall, Albert W.; Proschan, Frank

doi:10.1214/aoms/1177704147

Cited by 394 publications

(136 citation statements)

References 8 publications

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“…Since F (t) = r1 0 F r (t) P {R ∈ dr}, this is a special case of the result given in [1,Theorem 3.4].…”

Section: Propositionmentioning

confidence: 84%

Impact of Size-Based Scheduling on Flow Level Performance in Wireless Downlink Data Channels

Aalto¹,

Lassila²

2007

Lecture Notes in Computer Science

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Abstract.We analyze the impact of size-based scheduling on the flow level performance of elastic traffic in wireless downlink data channels. The impact is assessed by comparing the flow level delay of the simple RR scheduler to two optimized non-anticipating schedulers (FB and FB • ) and SRPT. The optimized distance-aware scheduler FB • is derived by applying the Gittins index approach. Our results show that for Paretotype file size distributions, the size-based information is more important than the location information. Additionally, FB not only decreases the overall mean delay, but it can also decrease considerably the mean delay of all users independently of their location.

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“…Since F (t) = r1 0 F r (t) P {R ∈ dr}, this is a special case of the result given in [1,Theorem 3.4].…”

Section: Propositionmentioning

confidence: 84%

Impact of Size-Based Scheduling on Flow Level Performance in Wireless Downlink Data Channels

Aalto¹,

Lassila²

2007

Lecture Notes in Computer Science

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“…Studies have shown that the volume of activation is smaller in the dual-task condition than in the sum of the two related single-task conditions (Just et al, 2001;Loose et al, 2003;Johnson and Zatorre, 2006;Newman et al, 2007). 10 Sub-additivity suggests the existence of "biological mechanisms that place an upper bound on the amount of cortical tissue that can be activated at any given time" (Just et al, 2001, p. 424)). 11 Some other studies highlight a significant behavioral interference when subjects perform the dual- 10 These studies measure activity in the sensory and association areas that are active in one (and only one) of the tasks.…”

Section: Evidence From Neurosciencementioning

confidence: 99%

“…10 Sub-additivity suggests the existence of "biological mechanisms that place an upper bound on the amount of cortical tissue that can be activated at any given time" (Just et al, 2001, p. 424)). 11 Some other studies highlight a significant behavioral interference when subjects perform the dual- 10 These studies measure activity in the sensory and association areas that are active in one (and only one) of the tasks. They are designed to minimize overlapping areas by choosing tasks that are known to recruit different brain systems (e.g., mental rotation of visually depicted objects and auditory comprehension).…”

Section: Evidence From Neurosciencementioning

confidence: 99%

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Resource Allocation in the Brain

Alonso

Brocas

Carrillo

2013

The Review of Economic Studies

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When an individual performs several tasks simultaneously, processing resources must be allocated to different brain systems to produce energy for neurons to fire. Following the evidence from neuroscience, we model the brain as an organization in which a coordinator allocates limited resources to the brain systems responsible for the different tasks. Systems are privately informed about the amount of resources necessary to perform their task and compete to obtain the resources. The coordinator arbitrates the demands while satisfying the resource constraint. We show that the optimal mechanism is to impose to each system with privately known needs a cap in resources that depends negatively on the amount of resources requested by the other system. This allocation can be implemented using a biologically plausible mechanism. Finally, we provide some implications of our theory: (i) performance is inversely related to the difficulty of the task and can be flawless for sufficiently simple tasks, (ii) the dynamic allocation rule exhibits inertia (current allocations are increasing in past needs), and (iii) different cognitive tasks are performed by different systems only if the tasks are sufficiently important.

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“…Increasing failure rate distribuitons have been widely studied. Some notable references are Barlow, Marshall and Proschan (1963), Barlow and Marshall (1964a,b), Barlow andProschan (1964), andBarlow (1965). A lucid discussion of the subject can be found in Barlow and Proschan (1975).…”

Section: 1) M(t) < +mentioning

confidence: 99%

Inequalities for Distributions With Increasing Failure Rate

Brown

1987

Contributions to the Theory and Application of Statistics

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Properties of Probability Distributions with Monotone Hazard Rate

Cited by 394 publications

References 8 publications

Impact of Size-Based Scheduling on Flow Level Performance in Wireless Downlink Data Channels

Impact of Size-Based Scheduling on Flow Level Performance in Wireless Downlink Data Channels

Resource Allocation in the Brain

Inequalities for Distributions With Increasing Failure Rate

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