Age of Information of Jackson Networks With Finite Buffer Size

We investigate the Age of Information (AoI) of Jackson Networks with finite buffer size. We provide a closed form expression of an upper bound of the average AoI by using Stochastic Hybrid Systems (SHS) along with linear algebra tools. Since the computation of the bound requires inverting a <inline-formula> <tex-math notation="LaTeX">${N}\,\,\times \,\,{N}$ </tex-math></inline-formula> matrix, where <inline-formula> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> is the number of queues in the network, we provide a simple iterative algorithm and prove its convergence with geometric convergence rate. Numerical results allow us to assess the accuracy of our model in various settings.

[1]  Roy D. Yates,et al.  Timely Updates By Multiple Sources: The M/M/1 Queue Revisited , 2020, 2020 54th Annual Conference on Information Sciences and Systems (CISS).

[2]  Roy D. Yates,et al.  Status Updates through Networks of Parallel Servers , 2018, 2018 IEEE International Symposium on Information Theory (ISIT).

[3]  J. R. Jackson.  Networks of Waiting Lines , 1957 .

[4]  Ness B. Shroff,et al.  Age-optimal Sampling and Transmission Scheduling in Multi-Source Systems , 2018, MobiHoc.

[5]  Shmuel Friedland,et al.  Nonnegative Matrix Inequalities and their Application to Nonconvex Power Control Optimization , 2011, SIAM J. Matrix Anal. Appl..

[6]  Roy D. Yates,et al.  Age of Information: An Introduction and Survey , 2020, IEEE Journal on Selected Areas in Communications.

[7]  Sennur Ulukus,et al.  Age of information in multihop multicast networks , 2018, Journal of Communications and Networks.

[8]  Anthony Ephremides,et al.  Effect of Message Transmission Path Diversity on Status Age , 2016, IEEE Transactions on Information Theory.

[9]  Eytan Modiano,et al.  Scheduling Policies for Minimizing Age of Information in Broadcast Wireless Networks , 2018, IEEE/ACM Transactions on Networking.

[10]  Ness B. Shroff,et al.  Optimizing data freshness, throughput, and delay in multi-server information-update systems , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[11]  Ness B. Shroff,et al.  The Age of Information in Multihop Networks , 2017, IEEE/ACM Transactions on Networking.

[12]  Ness B. Shroff,et al.  Age-optimal information updates in multihop networks , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[13]  Anthony Ephremides,et al.  The Age of Incorrect Information: A New Performance Metric for Status Updates , 2019, IEEE/ACM Transactions on Networking.

[14]  Elif Uysal-Biyikoglu,et al.  Age-optimal updates of multiple information flows , 2018, IEEE INFOCOM 2018 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS).

[15]  Anthony Ephremides,et al.  The Age of Updates in a Simple Relay Network , 2018, 2018 IEEE Information Theory Workshop (ITW).

[16]  Mor Harchol-Balter,et al.  Performance Modeling and Design of Computer Systems: Queueing Theory in Action , 2013 .

[17]  Anthony Ephremides,et al.  On the Age of Information in a CSMA Environment , 2020, IEEE/ACM Transactions on Networking.

[18]  Clement Kam,et al.  Age of Information for Queues in Tandem , 2018, MILCOM 2018 - 2018 IEEE Military Communications Conference (MILCOM).

[19]  Anthony Ephremides,et al.  Effect of message transmission diversity on status age , 2014, 2014 IEEE International Symposium on Information Theory.

[20]  Roy D. Yates,et al.  Real-time status: How often should one update? , 2012, 2012 Proceedings IEEE INFOCOM.

[21]  Sanjit Krishnan Kaul,et al.  Minimizing age of information in vehicular networks , 2011, 2011 8th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks.

[22]  Shahab Farazi,et al.  Fundamental Bounds on the Age of Information in General Multi-Hop Interference Networks , 2019, IEEE INFOCOM 2019 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS).

[23]  Gerard J. Foschini,et al.  A simple distributed autonomous power control algorithm and its convergence , 1993 .

[24]  Roy D. Yates,et al.  The Age of Information: Real-Time Status Updating by Multiple Sources , 2016, IEEE Transactions on Information Theory.

[25]  Roy D. Yates,et al.  Age of information in a network of preemptive servers , 2018, IEEE INFOCOM 2018 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS).