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- Title
Single-server queueing system with external and internal customers.
- Authors
TIKHONENKO, O.; ZIÓŁKOWSKI, M.
- Abstract
In the paper, we investigate a single-server queueing system with unlimited memory space and non-homogeneous customers (calls) of the two following types: 1) external customers that are served by the system under consideration, 2) internal customers that arrive and interrupt the service process only when an external customer is being served. The external customers appear according to a stationary Poisson process. Customers of each of the above-mentioned types are characterized by some random volume. The customer service time depends arbitrarily on its volume. Two schemes of customer service organization are analyzed. The non-stationary and stationary distributions of the total volume of customers present in the system are determined in terms of Laplace and Laplace-Stieltjes transforms. The stationary first and second moments of total customers volume are also calculated. The obtained results are used to approximate loss characteristics in analogous systems with limited buffer space. Numerical examples illustrating theoretical results are attached as well.
- Subjects
POISSON processes; LAPLACE distribution; TELECOMMUNICATION; APPLICATION software; IN-house services (Business)
- Publication
Bulletin of the Polish Academy of Sciences: Technical Sciences, 2018, Vol 66, Issue 4, p539
- ISSN
0239-7528
- Publication type
Article
- DOI
10.24425/124270