Abstract
A maximum likelihood estimator (MLE), a consistent asymptotically normal (CAN) estimator and asymptotic confidence limits for the expected number of customers in the system for a sequential two station, single server system with Poisson input and exponential service, where no queue is allowed in front of station 1 and atmost one customer is allowed to wait between the stations and with blocking are obtained.
Highlights
Most of the studies on several queueing models are confined to only obtaining expressions for transient or stationary solutions and do not consider the associated statistical inference problems
The following are some examples of tandem queues: a) In a manufacturing process, units must pass through a series of service channels, where each service channel performs a given task or job
Since the interarrival and service times are exponential, it follows that the process V (t) is a Markov Process with the infinitesimal generator Q given by Q
Summary
Most of the studies on several queueing models are confined to only obtaining expressions for transient or stationary (steady state) solutions and do not consider the associated statistical inference problems. A customer must pass through successively all the stations before completing his service Such situations are known as queues in series or tandem queues. The following are some examples of tandem queues: a) In a manufacturing process, units must pass through a series of service channels (work stations), where each service channel performs a given task or job. C) In a clinical physical examination procedure, a patient goes through a series of stages such as lab tests, ECG, chest X-ray etc In all these model structures, it is sufficient to know how many persons are there in the system and where they are. Station 1 is said to be blocked, if the customer in station 1 completes his service beforestation 2 becomes free and there is a customer waiting between the stations
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Pakistan Journal of Statistics and Operation Research
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
