TY - GEN
T1 - Modeling Interfering Sources in Shared Queues for Timely Computations in Edge Computing Systems
AU - Akar, Nail
AU - Bastopcu, Melih
AU - Ulukus, Sennur
AU - Başar, Tamer
N1 - Publisher Copyright:
© 2024 Copyright held by the owner/author(s).
PY - 2024/10/14
Y1 - 2024/10/14
N2 - Most existing stochastic models on age of information (AoI) focus on a single shared server serving status update packets from N > 1 sources where each packet update stream is Poisson, i.e., single-hop scenario. In the current work, we study a two-hop edge computing system for which status updates from the information sources are still Poisson but they are not immediately available at the shared edge server, but instead they need to first receive service from a transmission server dedicated to each source. For exponentially distributed and heterogeneous service times for both the dedicated servers and the edge server, and bufferless preemptive resource management, we develop an analytical model using absorbing Markov chains (AMC) for obtaining the distribution of AoI for any source in the system. Moreover, for a given tagged source, the traffic arriving at the shared server from the N − 1 un-tagged sources, namely the interference traffic, is not Poisson any more, but is instead a Markov modulated Poisson process (MMPP) whose state space grows exponentially with N. Therefore, we propose to employ a model reduction technique that approximates the behavior of the MMPP interference traffic with two states only, making it possible to approximately obtain the AoI statistics even for a very large number of sources. Numerical examples are presented to validate the proposed exact and approximate models.
AB - Most existing stochastic models on age of information (AoI) focus on a single shared server serving status update packets from N > 1 sources where each packet update stream is Poisson, i.e., single-hop scenario. In the current work, we study a two-hop edge computing system for which status updates from the information sources are still Poisson but they are not immediately available at the shared edge server, but instead they need to first receive service from a transmission server dedicated to each source. For exponentially distributed and heterogeneous service times for both the dedicated servers and the edge server, and bufferless preemptive resource management, we develop an analytical model using absorbing Markov chains (AMC) for obtaining the distribution of AoI for any source in the system. Moreover, for a given tagged source, the traffic arriving at the shared server from the N − 1 un-tagged sources, namely the interference traffic, is not Poisson any more, but is instead a Markov modulated Poisson process (MMPP) whose state space grows exponentially with N. Therefore, we propose to employ a model reduction technique that approximates the behavior of the MMPP interference traffic with two states only, making it possible to approximately obtain the AoI statistics even for a very large number of sources. Numerical examples are presented to validate the proposed exact and approximate models.
KW - absorbing Markov chains
KW - Age of information
KW - Markov modulated Poisson process
KW - two-hop status update systems
UR - http://www.scopus.com/inward/record.url?scp=85207089838&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85207089838&partnerID=8YFLogxK
U2 - 10.1145/3641512.3690166
DO - 10.1145/3641512.3690166
M3 - Conference contribution
AN - SCOPUS:85207089838
T3 - Proceedings of the International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc)
SP - 387
EP - 391
BT - MobiHoc 2024 - Proceedings of the 2024 International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile Computing
PB - Association for Computing Machinery
T2 - 2024 International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile Computing, MobiHoc 2024
Y2 - 14 October 2024 through 17 October 2024
ER -