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Fuzzy modeling of single server double orbit retrial queue

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Abstract

This paper investigates the single server double orbit retrial queueing model with customer’s discouragement in a fuzzy environment. The arriving customers in the system may be categorized into two classes, namely, ordinary customers and premium customers. The provision of double orbits (i) ordinary orbit and (ii) premium orbit, for the different class of customers, is made along with the realistic feature of balking and feedback behavior of the ordinary customers. On arrival, if both types of customers find the server busy and intend to join the system, then they are forced to shift their respective orbits. It is assumed that high (less) paying customers can be accommodated in a premium (ordinary) orbit. Further, based on Zadeh’s extension principle, \(\alpha\)-cut approach is implemented to construct a set of parametric nonlinear programming for performance indices, which is then solved by using concepts of calculus. Various performance indices including a mean number of customers and mean waiting time in the system are established for both in the crisp and fuzzy environment. Illustration examples are also explained by taking a triangular fuzzy number for input parameters.

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Authors and Affiliations

  1. Department of Mathematics and Humanities, SV National Institute of Technology Surat, Surat, India

    Sudeep Singh Sanga

  2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India

    Madhu Jain

Authors
  1. Sudeep Singh Sanga
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  2. Madhu Jain
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Correspondence to Sudeep Singh Sanga.

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Sanga, S.S., Jain, M. Fuzzy modeling of single server double orbit retrial queue. J Ambient Intell Human Comput 13, 4223–4234 (2022). https://doi.org/10.1007/s12652-022-03705-3

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