ScienceDirect IFAC-PapersOnLine 48-3 (2015) 1790–1795 Available online at www.sciencedirect.com 2405-8963 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2015.06.346 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Scheduling, MCBoS, processors, unavailabilities, unit, parallel, intrees. 1. INTRODUCTION A parallel application is commonly modeled by a prece- dence task graph G =(T,C ), where T represents the set of tasks and C represents the communications between tasks. In this problem, the graph is an intree where every task can have many predecessors but only one successor. Both execution and communication times are supposed to be unitary. This is called the UECT (Unit Execution and Communication Time) assumption. About the communications: • The communications between tasks executed on the same processor are negligible (not taken into ac- count). • The ability of a processor to perform both compu- tations and communications simultaneously is called the overlap assumption. In this paper, we suppose that the overlap of the communications by computa- tions is possible. In this paper, the scheduling of UECT intrees on two pro- cessors is treated where one of these is subject to periods of unavailabilities. The aim is to minimise the duration of the schedule or makespan denoted C max . The considered problem is denoted P 2 ,NC |intree, p i =1,c i =1|C max . The new proposed algorithm denoted MCBoS (Modified CBoS) builds optimal schedules (when the root is on the processor P 1 ). The paper is organized as follows: in the section 2, previous works are presented. Section 3 and 4 are devoted to the proposed algorithm. Sections 5 presents the optimality proof and finally section 6 concludes the paper. 2. RELATED WORKS 2.1 Problems with communications This section presents the problem of scheduling UECT trees on two identical processors without unavailabilities. For m machines, the problem of scheduling UECT trees can be solved by a dynamic programming algorithm of complexity o(n 2(m-1) ). For 2 machines, the problem is denoted P 2 |tree, p i = 1,c i =1|C max . To resolve this scheduling problem, many algorithms with different strategies have been developped and gave the same optimality result. Veldhorst and Lawler M.Veldhorst (1993) E.L.Lawler (1993) are based on list strategy and Guinand F.Guinand and D.Trystram (2000) and picouleau (C.Picouleau, 1993) is based on a clustering strategy by his algorithm denoted CBoS (Clusters Based on Subtrees). In this section we present the CBoS (Clusters Based on Subtrees) algorithm used to scheduling intrees on two identical processors. It focuses on the allocation of clusters to processor P 2 (the root is allocated to the processor P 1 ). The clusters are subtrees and determined according to a load-balancing criterion. The clustering strategy is used to minimise inter-processors communications and the makespan. The schedules obtained by CBoS are Processor * UR MARS, FSM, Universite de Monastir, ISITCom, Universite de Sousse(e-mail:khawlaabdellafo@gmail.com). ** Normandie University, Le Havre, France (e-mail: eric.sanlaville@univ-lehavre.fr) *** College of Computers and Information Technology Taif University,Kingdom of Saudi Arabia., (e-mail: a.mahjoub@tu.edu.sa) **** UR MARS, FSM, Universite de Monastir, ISITCom, Universite de Sousse(e-mail:Ouajdi.Korbaa@centraliens-lille.org). Abstract: In this paper a new polynomial scheduling algorithm is presented. It is used for scheduling Unit Execution and Communication Time (UECT) intrees on two identical processors where one of these is subject to periods of unavailabilities. The optimality criterion is the makespan. Scheduling UECT trees with Communication Delays on Two Processors with Unavailabilities Khaoula Ben Abdellafou * Eric Sanlaville ** Amine Mahjoub *** Ouajdi Korbaa ****