Article Performance Analysis of M/M (a,b) /1 Queuing Model with Balking and State-dependent Reneging and Service Kuntal Bakuli 1 Manisha Pal 1 Calcutta Statistical Association Bulletin 69(1) 76–86 © 2017 Calcutta Statistical Association, Kolkata SAGE Publications sagepub.in/home.nav DOI: 10.1177/0008068317696551 http://csa.sagepub.com Abstract The article investigates a M/M (a,b) /1 queuing model with impatient customers. The size of a batch taken up for service depends on the number of customers present in the waiting line. The server serves a minimum of ‘‘a’’ and a maximum of ‘‘b’’ customers at a time. The service time is assumed to be exponentially distributed with mean dependent on the batch size. Customers arrive to the system as a Poisson process, and may leave on finding a long queue or may renege after waiting in the queue for an exponentially distributed time. The model is analyzed to find different measures of effectiveness of the system. A new measure of performance is also discussed. The approach adopted for analysis of the model is based on embedded Markov chain. Keywords Bulk service, balking and reneging, Poisson arrival, embedded Markov chain, performance measures AMS 2000 subject classification: 60J10 1. Introduction Bulk service and bulk arrival are common phenomena in real life. Some common examples of systems with bulk service are telecommunication, transportation, production, airline scheduling, and elevators. Over the past few decades, much study has been carried out on bulk service queuing systems. Jaiswal [1] discussed a bulk service queue with variable capacity. Powell and Humblet [2] investigated general control strategy for bulk service queues. Downton [3] studied the waiting time in bulk service model. Jayaraman, Nadarajan, and Sitrarasu [4] analyzed a general bulk service system with arrival rate dependent on server breakdown. Dshalalow [5] explored the D-policy for bulk queuing system. Jain and Singh [6] investigated state-dependent bulk service queue with delayed vacations. However, very few authors considered bulk 1 Department of Statistics, University of Calcutta, India. Corresponding author: Kuntal Bakuli, Department of Statistics, University of Calcutta, Kolkata-700 019, India. E-mail: kuntalbakuli17@gmail.com