The first decade of G-networks

This special issue of the European Journal of Operational Research deals with a class of queueing networks, sometimes called ``G-networks'', which include a variety of unusual ``customers''. We introduced these models in a publication some 10 years ago in 1989 [1], and in their 10th year we welcome the hospitality of the European Journal of Operational Research to brie ̄y consider the outcome of the resulting research. Traditionally, customers in queueing networks request service, obtain service (or a rejected), and move from one queue to another until completion. In addition to these conventional customers, Gnetworks [1,3±7,9,10] include other customers which can carry out operations such as: · destroy other customers as they arrive to a queue, either individually or in batch mode, · trigger the motion of customers from one queue to another and even do this repeatedly in some kind of list mode, · remove work rather than customers, and many variants thereof which include multiple classes of customers. The initial papers demonstrated that these networks had product form, but also showed that the usual network trac equations in such cases would be in general non-linear. Several authors also looked at single server versions of these models with fairly general arrival and service processes. These models have generated a pleasantly large interest in the queueing theory community with well over a 100 publications by very capable researchers such as J.R. Artalejo, R. Schassberger, K. Sigman, W. Henderson, P. Taylor, M. Miyazawa, P. Glynn, P.G. Harrison, R. Boucherie, J.M. Fourneau, O. Boxma, P. Glynn, X. Chao, M. Pinedo, R. Serfozo, A. Labed, A. Gomez-Gorral, E. Pitel, B.S. Northcote, H. Shachnai, G. Jain, D. Verch ere, L. Kloul, and many others. This special issue conducts a survey of many of these ideas and results and suggests some interesting directions for further research and applications. The paper ``G-networks: A versatile approach for work removal in queueing networks'', by J.R. Artalejo (Spain), surveys some of these publications and the main related ideas which have been presented in the queueing network community. The paper on ``Multiple class G-networks with list oriented deletions'', by J.M. Fourneau, L. Kloul, D. Verch ere (France), considers G-networks with iterated deletions and demonstrates some related product form results. The paper ``Reliability modelling using G-queues'', by Peter G. Harrison, Naresh M. Patel, Edwige Pitel (UK, USA, France), considers models for breakdown and repair in single server queues using G-queues. Rather than dealing speci®cally with theoretical developments, the next four papers address a variety of application areas. The work on ``Reinforcement learning with internal expectation for the random neural network'', by Ugur Halici (Turkey), interprets a network with positive and European Journal of Operational Research 126 (2000) 231±232 www.elsevier.com/locate/dsw