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In this paper, we analyze the queueing behaviour of wavelength division multiplexing (WDM) Internet router employing partial buffer sharing (PBS) mechanism with self-similar traffic input. In view of WDM technology in networking, each output port of the router is modelled as multi-server queueing system. To guarantee the quality of service (QoS) in Broadband integrated services digital network (B-ISDN), PBS mechanism is a promising one. As Markov modulated Poisson process (MMPP) emulates self-similar Internet traffic, we can use MMPP as input process of queueing system to investigate queueing behaviour of the router. In general, as network traffic is asynchronous (unslotted) and of variable packet lengths, service times (packet lengths) are assumed to follow Erlang-k distribution. Since, the said distribution is relatively general compared to deterministic and exponential. Hence, specific output port of the router is modelled as MMPP/Ek/s/C queueing system. The long-term performance measures namely high priority and low priority packet loss probabilities and the short-term performance measures namely mean lengths of critical and non-critical periods against the system parameters and traffic parameters are computed by means of matrix-geometric methods and approximate Markovian model. This kind of analysis is useful in dimensioning the router under self-similar traffic input employing PBS mechanism to provide differentiated services (DiffServ) and QoS guarantee.

applied mathematics

Performance Analysis of Wavelength Division Multiplexing Asynchronous Internet Router Employing Space Priority Mechanism under Self-Similar Traffic Input—Multi-Server Queueing System with Markovian Input and Erlang-k Services