Performance Evaluation of Parallel-processing Networked System with Linear Time Delay Sohag Kabir 1 A S M Ashraful Alam 2 Tanzima Azad 3 1 Department of Computer Science, University of Hull, Hull, United Kingdom Email: s.kabir@hull.ac.uk 2 Department of Computer Science, University of Otago, Dunedin, New Zealand Email: aalam@cs.otago.ac.nz 3 Department of CSE, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh Email: azad.tanzima@dbbl.com.bd Abstract Time delays in system subcomponents or control may re- sult into unacceptable system operation or uncertainty in specialised technical systems like aircraft control, plant control, robotics, etc. In parallel computing, different computing subunits share their tasks to balance loads to increase performance and throughput. To be able to do so, subsystems have to communicate among themselves, which adds further delay on top of the existing system delay. It is possible to improve performance and stabil- ity of the whole system, by designing observer for every subsystem in the system, overseeing the system-state and compensating for existing time-delay. This paper reviews the present literature to identify a linear time-delay sys- tem for load balancing and evaluates the stability and load- balancing performance of the system with and without an observer. Stability is analysed in terms of oscillation in the system responses and performance is evaluated as the speed of load-balancing operation. Keywords: Networked System, Parallel Computing, Time-delay Systems, Cluster Computing, Load Balancing 1 Introduction Parallel computing is the dominant paradigm in large com- plex systems architecture. Simultaneous calculations are carried out in parallel-computing systems, following the principle that large problems can be split into smaller ones and can be solved concurrently. A busy computing unit may share some of its load with a relatively idle com- puting unit, resulting in a significant increase in system performance and throughput. However, in a network envi- ronment, information about the workload on subunits are not instantly available to other subunits due to time-delay experienced during communication, which affects system performance adversely. Time-delay systems, generally known as systems with deceased time or after impact, transmissible systems, sys- tems of equations with deviation in argument or systems of differential-difference equation. They are a constituent of infinite dimensional functional differential equations (FDEs) which are opposite of ordinary differential equa- tions (ODEs) (Richard 2003). In the clustered machine en- Copyright c 2015, Australian Computer Society, Inc. This paper ap- peared at the 13th Australasian Symposium on Parallel and Distributed Computing (AusPDC 2015), Sydney, Australia, January 2015. Con- ferences in Research and Practice in Information Technology (CRPIT), Vol. 163, Bahman Javadi and Saurabh Kumar Garg, Ed. Reproduction for academic, not-for-profit purposes permitted provided this text is in- cluded. vironment, additional communication delay is inevitable. The needs for observing time-delay in systems comes from the real demand of system tracking, control and/or identification of system failure. Feedbacks are important in mission critical systems. The difficulties concerning sensitivity and robustness of the feedback system with respect to time delays has at- tracted much attention as feedback control systems add additional delays. The adverse effect of time-delay can be minimised by observing the states of time-delay systems and then utilising the information to model a linear time- delay system aimed at designing observers for all subsys- tems to minimise delays and increase stability. This paper briefly reviews the literature to identify a networked parallel processing system with linear time- delay. Then the system is modelled and simulated using SIMULINK to analyse the stability and performance of the system in performing load balancing operation. Stabil- ity is analysed in terms of oscillation in system responses and performance is measured as speed of operation, i.e. how quickly the system can balance loads among subsys- tems. We have designed the observers for all subsystems of the parallel processing linear time delay system based on the findings of these analyses. Observer of each sub- system estimates some necessary values for the subsystem to allow it to work independently without communicating with other subsystems thus minimising the effect of time- delay in the system performance. To evaluate the system performance the system with observers are modelled and simulated in SIMULINK. The rest of the paper is organized as follows: Section 2 presents the background study and literature review on time-delay systems, observer design and load-balancing techniques. The parallel processing linear time-delay sys- tem is described, modelled, simulated, and results of the simulation are shown in section 3. In section 4, observers are designed, system with observers is modelled, simu- lated and the results of the simulation are presented. Sec- tion 5 presents the discussion of the results obtained dur- ing the analysis. Finally, concluding remarks are pre- sented in section 6. 2 BACKGROUND STUDY AND LITERATURE REVIEW 2.1 Time-Delay Systems: Their Mathematical Mod- els and Observers Time-delay is experienced frequently in various control systems; either in the control input, the system states or processing (Fridman & Shaked 2002). Time-delay can be a source of instability and is very important for perfor- Proceedings of the 13th Australasian Symposium on Parallel and Distributed Computing (AusPDC 2015), Sydney, Australia, 27 - 30 January 2015 97