Product-Form Solution for Cascade Networks With Intermittent Energy

The power needs of digital devices, their installation in locations where it is difficult to connect them to the power grid and the difficulty of frequently replacing batteries, create the need to operate digital systems with harvested energy. In such cases, local storage batteries must overcome the intermittent nature of the energy supply. System performance then depends on the intermittent energy supply, possible energy leakage, and system workload. Queueing networks with product-form solution (PFS) are standard tools for analyzing the performance of interconnected systems, and predicting relevant performance metrics including job queue lengths, throughput, and system turnaround times and delays. However, existing queueing network models assume unlimited energy availability, whereas intermittently harvested energy can affect system performance due to insufficient energy supply. Thus, this paper develops a new PFS for the joint probability distribution of energy availability, and job queue length for an N-node tandem system. Such models can represent production lines in manufacturing systems, supply chains, cascaded repeaters for optical links, or a data link with multiple input data ports that feeds into a switch or server. Our result enables the rigorous computation of the relevant performance metrics of such systems operating with intermittent energy.

[1]  G. J. A. Stern,et al.  Queueing Systems, Volume 2: Computer Applications , 1976 .

[2]  Koushik Kar,et al.  Optimal Routing and Scheduling in Multihop Wireless Renewable Energy Networks , 2013, IEEE Transactions on Automatic Control.

[3]  Yasin Murat Kadioglu FINITE CAPACITY ENERGY PACKET NETWORKS , 2017, Probability in the Engineering and Informational Sciences.

[4]  Erol Gelenbe,et al.  Packet transmission with K energy packets in an energy harvesting sensor , 2016 .

[5]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[6]  Yves Dallery,et al.  Measurement and Management of Supply Chain Performance: A Benchmarking Study , 2014, APMS.

[7]  Wu He,et al.  Internet of Things in Industries: A Survey , 2014, IEEE Transactions on Industrial Informatics.

[8]  Elif Uysal-Biyikoglu,et al.  Energy-efficient packet transmission over a wireless link , 2002, TNET.

[9]  Erol Gelenbe,et al.  Synchronising Energy Harvesting and Data Packets in a Wireless Sensor , 2015 .

[10]  Elizabeth Varki Mean value technique for closed fork-join networks , 1999, SIGMETRICS '99.

[11]  Leon F. McGinnis,et al.  Interpolation approximations for queues in series , 2013 .

[12]  Charles H. Sauer,et al.  The Tree MVA Algorithm , 1985, Perform. Evaluation.

[13]  Erol Gelenbe,et al.  The impact of information technology on energy consumption and carbon emissions , 2015, UBIQ.

[14]  Erol Gelenbe,et al.  Interconnected Wireless Sensors with Energy Harvesting , 2015, ASMTA.

[15]  Armando N. Pinto,et al.  Optical Networks: A Practical Perspective, 2nd Edition , 2002 .

[16]  Peter G. Harrison,et al.  Methodological construction of product-form stochastic Petri nets for performance evaluation , 2012, J. Syst. Softw..

[17]  Min Chen,et al.  A Survey on Internet of Things From Industrial Market Perspective , 2015, IEEE Access.

[18]  Ashok K. Agrawala,et al.  Analysis of the Fork-Join Queue , 1989, IEEE Trans. Computers.

[19]  Laura Strauss,et al.  Optical Networks A Practical Perspective , 2016 .

[20]  Erol Gelenbe,et al.  Energy packet networks: adaptive energy management for the cloud , 2012, CloudCP '12.

[21]  Yves Dallery,et al.  Manufacturing flow line systems: a review of models and analytical results , 1992, Queueing Syst. Theory Appl..

[22]  Anurag Agarwal,et al.  The Internet of Things—A survey of topics and trends , 2014, Information Systems Frontiers.

[23]  James R. Jackson,et al.  Jobshop-Like Queueing Systems , 2004, Manag. Sci..

[24]  Leandros Tassiulas,et al.  Control of wireless networks with rechargeable batteries [transactions papers] , 2010, IEEE Transactions on Wireless Communications.

[25]  E. Gelenbe G-networks by triggered customer movement , 1993 .

[26]  Roger Wattenhofer,et al.  Towards a zero-configuration wireless sensor network architecture for smart buildings , 2009, BuildSys '09.

[27]  C. E. Koksal,et al.  Near Optimal Power and Rate Control of Multi-Hop Sensor Networks With Energy Replenishment: Basic Limitations With Finite Energy and Data Storage , 2012, IEEE Transactions on Automatic Control.

[28]  Erol Gelenbe,et al.  Steady-state solution of probabilistic gene regulatory networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Sherali Zeadally,et al.  Enabling Technologies for Green Internet of Things , 2017, IEEE Systems Journal.

[30]  P. Konstantopoulos,et al.  Stationary and stability of fork-join networks , 1989, Journal of Applied Probability.

[31]  Kaibin Huang,et al.  Energy Harvesting Wireless Communications: A Review of Recent Advances , 2015, IEEE Journal on Selected Areas in Communications.

[32]  Deniz Gündüz,et al.  Designing intelligent energy harvesting communication systems , 2014, IEEE Communications Magazine.

[33]  Peter G. Harrison,et al.  Analysis of stochastic Petri nets with signals , 2012, Perform. Evaluation.