The erlang odel for a fragment of SDN architecture

Abstract

A fragment of a Software-Defined Networking (SDN) architecture with the functionality of switches and controllers is described as the mathematical model of a multiphase queueing system with losses at each phase. In the IETF draft “Address Resolution Delay in SDN” (also, see ITU-R M.2083-0), it was recommended to reduce network delay within a single SDN segment from 50 ms to 1 ms. This performance index considerably depends on the characteristics of the software and hardware system of SDN networks as well as on the processes of interaction between switches and controller. However, the service time and hence the processing delays for packet flows are not regulated by the suppliers of switching equipment (e.g., Cisco Catalyst 3750 switches), which makes it difficult to determine the probabilistic and time characteristics of networks during the design stage and also to formalize any suggestions on improving the performance of network elements. The models presented in this paper are based on the classical queueing theory and Laplace transforms. In this case, the relation between the stages of packets processing on network devices has little significance, and therefore the performance indices are obtained in terms of single-phase network parameters. The mean service time and the mean number of packets in a network are calculated as functions of the load of network devices. Also, analytical expressions for determining the mean loss ratio of network packets at each phase of processing by a switch are derived