NDLI: Analysis of the dynamics of social queues by quasi-birth-and-death processes (abstract only)

Content Provider	ACM Digital Library
Author	Field, Jeremy Toyoizumi, Hiroshi
Abstract	A wide variety of animals are known to form simple hierarchical groups called social queues, where individuals inherit resources or social status in a predictable order. Queues are often age-based, so that a new individual joins the end of the queue on reaching adulthood, and must wait for older individuals to die in order to reach the front of the queue. While waiting, an individual may work for her group, in the process often risking her own survival and hence her chance of inheritance. Eventually, she may survive to reach the head of the queue and becomes the dominant of the group. Queueing has been particularly well-studied in hover wasps (Hymenoptera: Stenogastrinae). In hover wasp social groups, only one female lays eggs, and there is a strict, age-based queue to inherit the reproductive position. While the dominant individual (queen) concentrates on breeding, subordinate helpers risk death by foraging outside the nest, but have a slim chance of eventually inheriting dominance. Some explanations for this altruistic behavior and for the stability of social queues have been proposed and analyzed [1, 2]. Since both the productivity of the nest and the chance to inherit the dominant position depend critically on group size, queueing dynamics are crucial for understanding social queues, but detailed analysis is lacking. Here, using hover wasps as an example, we demonstrate that the application of Little's formula [3] and quasi-birth-and-death (QBD) processes are useful for analyzing queueing dynamics and the population demographics of social queues. Let (L(t),M(t)) be the number of adults and brood (eggs, larvae and pupae) in a nest at time t. We model the vector (L(t),M(t)) as a QBD process starting from the state (L(0),M(0)) = (1, 0) to analyze the nest history of a social queue. The boundary state {L(t) = 0}, which corresponds to the termination of the nest, is regarded as the taboo state of this QBD process. Let Q be the transition rate matrix of the taboo process. By choosing different Q, we can set various conditions for the social queue. By using standard technique such as calculating Q?1, we can estimate and compare the productivity of the nest in wide variety of social queues in different queueing and environmental conditions. Our work leads to better understanding of how environmental conditions and strategic decision-making by individuals interact to produce the observed group dynamics; and in turn, how group dynamics affects individual decision-making.
Starting Page	29
Ending Page	30
Page Count	2
File Format	PDF
ISSN	01635999
DOI	10.1145/2185395.2185420
Journal	ACM SIGMETRICS Performance Evaluation Review (PERV)
Volume Number	39
Issue Number	4
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-01-10
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Computer Networks and Communications Hardware and Architecture Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Two-dimensional fluid queues with temporary assistance (abstract only)

A self-promoting priority model for transplant queues (abstract only)

Tail asymptotics of the stationary distribution for M/M-JSQ with k parallel queues (abstract only)

Queues with Redundancy:Latency-Cost Analysis

Bilateral matrix-exponential distributions (abstract only)

Moment distributions of phase-type (abstract only)

Exact Analysis of Some Split-Merge Queues

Majorization and Extremal PH-Distributions (abstract only)

The algorithmization of mathematics:the story of stochastic models (abstract only)

Analysis of the dynamics of social queues by quasi-birth-and-death processes (abstract only)

Similar Documents

Two-dimensional fluid queues with temporary assistance (abstract only)

A self-promoting priority model for transplant queues (abstract only)

Tail asymptotics of the stationary distribution for M/M-JSQ with k parallel queues (abstract only)

Queues with Redundancy:Latency-Cost Analysis

Bilateral matrix-exponential distributions (abstract only)

Moment distributions of phase-type (abstract only)

Exact Analysis of Some Split-Merge Queues

Majorization and Extremal PH-Distributions (abstract only)

The algorithmization of mathematics:the story of stochastic models (abstract only)

Analysis of the dynamics of social queues by quasi-birth-and-death processes (abstract only)