Abstract
In this paper, a discrete-time single-server queue is considered with an uncorrelated message arrival process and an uncorrelated server interruption process. The length of the messages is modeled as a series of positive i.i.d. random variables and two operation modes are considered. In continue after interruption mode (CAI) the processing of an interrupted message resumes with the next packet of this message. In repeat after interruption mode (RAI), the complete message is reprocessed after a server interruption. Using a generating-functions approach, explicit expressions for the mean and variance of buffer occupancy and message delay are derived for both operation modes. For illustration purposes, a discrete-time Pois-Geo-1 system is then evaluated. Scope and purpose Discrete-time queueing theory has gained a lot of interest recently to describe queueing related phenomena in an environment where time is slotted, such as various digital computer and communication systems including mobile and B-ISDN networks based on asynchronous transfer mode technology. This work focuses on a discrete-time queueing system with server interruptions, which can occur when several users have to share a common resource, or when this resource is temporarily unavailable due to external causes such as maintenance or system failures. The contribution of this paper mainly lies in the model that is considered, the solution method that is applied, as well as the results that are generated. First, we want to introduce a model with an interrupted service process that allows us to compare an environment where interrupted messages must be retransmitted with the situation where this is not the case. Second, we will show that a generating-functions approach is extremely suitable for solving such a queueing model. And finally, we want to establish closed-form formulas in terms of the system parameters that enable us to assess the system performance for the two transmission modes that are considered.
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 callDisclaimer: 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.
