Abstract
We consider a tandem queueing system with session arrivals. Session means a group of customers which should be sequentially processed in the system. In contrast to the standard batch arrival when a whole group of customers arrives into the system at one epoch, we assume that the customers of an accepted session arrive one by one in exponentially distributed times. Generation of sessions at the first stage is described by a Batch Markov Arrival Process (BMAP). At the first stage of tandem, it is determined whether a session has the access to the second stage. After the first stage the session moves to the second stage or leaves the system. At the second stage having a finite buffer the customers from sessions are serviced. A session consists of a random number of customers. This number is geometrically distributed and is not known at a session arrival epoch. The number of sessions, which can be admitted into the second stage simultaneously, is subject to control. An accepted session can be lost, with a given probability, in the case of any customer from this session rejection.
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Lucantoni, D.: New results on the single server queue with a batch Markovian arrival process. Communication in Statistics-Stochastic Models 7, 1–46 (1991)
Ferng, H.W., Chang, J.F.: Departure processes of BMAP/G/1 queues. Queueing Systems 39, 100–135 (2001)
Dudin, A.: Optimal multithreshold control for a BMAP/G/1 queue with N service modes. Queueing Systems 30, 273–287 (1998)
Dudin, A.N., Nishimura, S.: Optimal Control for a BMAP/G/1 Queue with Two Service Modes. Mathematical Problems in Engineering 5, 255–273 (1999)
Chang, S.H., Takine, T., Chae, K.C., Lee, H.W.: A unified queue length formula for BMAP/G/1 queue with generalized vacations. Stochastic Models 18, 369–386 (2002)
Shin, Y.W.: BMAP/G/1 queue with correlated arrivals of customers and disasters. Operations Research Letters 32, 364–373 (2004)
Saffer, Z., Telek, M.: Unified analysis of BMAP/G/1 cyclic polling models. Queueing Systems 64, 69–102 (2010)
Dudin, A., Klimenok, V.: Queueing system BMAP/G/1 with repeated calls. Mathematical and Computer Modelling 30, 115–128 (1999)
Dudin, A.N., Krishnamoorthy, A., Joshua, V.C., Tsarenkov, G.V.: Analysis of the BMAP/G/1 retrial system with search of customers from the orbit. European Journal of Operational Research 157, 169–179 (2004)
Dudin, A., Semenova, O.: A stable algorithm for stationary distribution calculation for a BMAP/SM/1 queueing system with Markovian arrival input of disasters. Journal of Applied Probability 41, 547–556 (2004)
Semenova, O.V.: Optimal control for a BMAP/SM/1 queue with map-input of disasters and two operation modes. RAIRO - Operations Research 38, 153–171 (2004)
Choi, B.D., Chung, Y.H., Dudin, A.N.: BMAP/SM/1 retrial queue with controllable operation modes. European Journal of Operational Research 131, 16–30 (2001)
Blondia, C.: The N/G/1 finite capacity queue. Communications in Statistics - Stochastic Models 5, 273–274 (1989)
Dudin, A.N., Nishimura, S.: Optimal hysteretic control for a BMAP/SM/1/N queue with two operation modes. Mathematical Problems in Engineering 5, 397–420 (2000)
Dudin, A.N., Klimenok, V.I., Tsarenkov, G.V.: Characteristics calculation for single-server queue with the BMAP input, SM service and finite buffer. Automation and Remote Control 63, 1285–1297 (2002)
Dudin, A.N., Shaban, A.A., Klimenok, V.I.: Analysis of a BMAP/G/1/N queue. International Journal of Simulation: Systems, Science and Technology 6, 13–23 (2005)
Kim, C.S., Klimenok, V., Tsarenkov, G., Breuer, L., Dudin, A.: The BMAP/G/1 → ∙ /PH/1/M tandem queue with feedback and losses. Performance Evaluation 64, 802–818 (2007)
Klimenok, V., Breuer, L., Tsarenkov, G., Dudin, A.: The BMAP/G/1/N → ∙ /PH/1/M tandem queue with losses. Performance Evaluation 61, 17–40 (2005)
Kim, C.S., Klimenok, V., Taramin, O.: A tandem retrial queueing system with two Markovian flows and reservation of channels. Computers and Operations Research 37, 1238–1246 (2010)
Kim, C., Dudin, A., Klimenok, V., Taramin, O.: A tandem BMAP/G/1 → ∙ /M/N/0 queue with group occupation of servers at the second station. Mathematical Problems in Engineering 2012, art. no. 324604 (2012)
Lee, M.H., Dudin, S., Klimenok, V.: Queueing Model with Time-Phased Batch Arrivals. In: Mason, L.G., Drwiega, T., Yan, J. (eds.) ITC 2007. LNCS, vol. 4516, pp. 719–730. Springer, Heidelberg (2007)
Kim, C.S., Dudin, S.A., Klimenok, V.I.: The MAP/PH/1/N queue with time phased arrivals as model for traffic control in telecommunication networks. Performance Evaluation 66, 564–579 (2009)
Kim, C.S., Dudin, A., Dudin, S., Klimenok, V.: A Queueing System with Batch Arrival of Customers in Sessions. Computers and Industrial Engeneering 62, 890–897 (2012)
Graham, A.: Kronecker Products and Matrix Calculus with Applications. Ellis Horwood, Chichester (1981)
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Dudin, S., Dudina, O. (2013). A Tandem Queueing System with Batch Session Arrivals. In: Dudin, A., Klimenok, V., Tsarenkov, G., Dudin, S. (eds) Modern Probabilistic Methods for Analysis of Telecommunication Networks. BWWQT 2013. Communications in Computer and Information Science, vol 356. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35980-4_8
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DOI: https://doi.org/10.1007/978-3-642-35980-4_8
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