  This paper studies an infinite buffer single server queueing model with
exponentially distributed service times and negative arrivals. The ordinary
(positive) customers arrive in batches of random size according to renewal
arrival process, and joins the queue/server for service. The negative arrivals
are characterized by two independent Poisson arrival processes, a negative
customer which removes the positive customer undergoing service, if any, and a
disaster which makes the system empty by simultaneously removing all the
positive customers present in the system. Using the supplementary variable
technique and difference equation method we obtain explicit formulae for the
steady-state distribution of the number of positive customers in the system at
pre-arrival and arbitrary epochs. Moreover, we discuss the results of some
special models with or without negative arrivals along with their stability
conditions. The results obtained throughout the analysis are computationally
tractable as illustrated by few numerical examples. Furthermore, we discuss the
impact of the negative arrivals on the performance of the system by means of
some graphical representations.
