This paper considers a discrete-time queueing system in which an arriving customer can decide to follow a last come first served (LCFS) service discipline or to become a negative customer that eliminates the one at service, if any. After service completion, the server can opt for a vacation time or it can remain on duty. Changes in the vacation times as well as their associated distribution are thoroughly studied. An extensive analysis of the system is carried out and, using a probability generating function approach, steady-state performance measures such as the first moments of the busy period of the queue content and of customers delay are obtained. Finally, some numerical examples to show the influence of the parameters on several performance characteristics are given.
Alfa, A. (2010). Queueing Theory for Telecommunications 1: Discrete Time Modelling of a Single Node System, Springer, New York, NY.
Artalejo, J. (2000). G-networks: A versatile approach for work removal in queueing networks, European Journal of Operational Research 126(2): 233-249.
Atencia, I. (2014). A discrete-time system with service control and repairs, International Journal of Applied Mathematics and Computer Science 24(3): 471-484, DOI: 10.2478/amcs-2014-0035.
Atencia, I. (2015). A discrete-time system queueing system with server breakdowns and changes in the repair times, Annals of Operations Research 235(1): 37-49.
Atencia, I. and Moreno, P. (2004). The discrete-time Geo/Geo/1 queue with negative customers and disasters, Computers and Operations Research 31(9): 1537-1548.
Atencia, I. and Moreno, P. (2005). A single-server G-queue in discrete-time with geometrical arrival and service process, Performance Evaluation 59(1): 85-97.
Bocharov, P.P., D’Apice, C., Pechinkin, A.V. and Salerno, S. (2004). Queueing Theory: Modern Probability and Statistics, VSP, Utrecht/Boston, MA.
Bruneel, H. and Kim, B. (1993). Discrete-time Models for Communication Systems Including ATM, Kluwer Academic Publishers, New York, NY.
Brush, A., Bongshin, L., Ratul, M., Sharad, A., Stefan, S. and Colin, D. (2011). Home automation in the wild: Challenges and opportunities, ACM Conference on Computer-Human Interaction, Vancouver, Canada, pp. 2115-2124.
Cascone, A., Manzo, P., Pechinkin, A. and Shorgin, S. (2011). A Geom/G/1/n system with LIFO discipline without interrupts and constrained total amount of customers, Automation and Remote Control 72(1): 99-110.
Chao, X., Miyazawa, M. and Pinedo, M. (1999). Queueing Networks: Customers, Signals and Product Form Solutions, John Wiley and Sons, Chichester.
Cooper, R. (1981). Introduction to Queueing Theory, 2nd Edn., North-Holland, New York, NY.
Fiems, D. and Bruneel, H. (2013). Discrete-time queueing systems with Markovian preemptive vacations, Mathematical and Computer Modelling 57(3-4): 782-792.
Fiems, D., Steyaert, B. and Bruneel, H. (2002). Randomly interrupted GI/G/1 queues: Service strategies and stability issues, Annals of Operations Research 112(1): 171-183.
Gelenbe, E. and Labed, A. (1998). G-networks with multiple classes of signals and positive customers, European Journal of Operational Research 108(1): 293-305.
Guzmán-Navarro, F. andMerino-Córdoba, S. (2015). Gestión de la energía y gestión técnica de edificios, 1st Edn., RA-MA, Málaga.
Harrison, P.G., Patel, N.M. and Pitel, E. (2000). Reliability modelling using G-queues, European Journal of Operational Research 126(2): 273-287.
Hochendoner, P., Curtis, O. and Mather, W.H. (2014). A queueing approach to multi-site enzyme kinetics, Interface Focus 4(3): 1-9, DOI: 10.1098/rsfs.2013.0077.
Hunter, J. (1983). Mathematical Techniques of Applied Probability, Academic Press, New York, NY.
Kim, T., Bauer, L., Newsome, J., Perrig, A. and Walker, J. (2010). Challenges in access right assignment for secure home networks, HotSec 2010, CA, USA, pp. 1-6.
Kleinrock, L. (1976). Queueing Theory, John Wiley and Sons, New York, NY.
Krishnamoorthy, A., Gopakumar, B. and Viswanath Narayanan, V. (2012). A retrial queue with server interruptions, resumption and restart of service, Operations Research International Journal 12(2): 133-149.
Krishnamoorthy, A., Pramod, P. and Chakravarthy, S. (2013). A note on characterizing service interruptions with phase-type distribution, Journal of Stochastic Analysis and Applications 31(4): 671-683.
Krishnamoorthy, A., Pramod, P. and Chakravarthy, S. (2014). A survey on queues with interruptions, TOP 22(1): 290-320.
Lakatos, L., Szeidl, L. and Telek, M. (2013). Introduction to Queueing Systems with Telecommunication Applications, Springer, New York, NY.
Lucero, S. and Burden, K. (2010). Home Automation and Control, ABI Research, New York, NY.
Meykhanadzhyan, L.A., Milovanova, T.A., Pechinkin, A.V. and Razumchik, R.V. (2014). Stationary distribution in a queueing system with inverse service order and generalized probabilistic priority, Informatika Primenenia 8(3): 28-38, (in Russian).
Milovanova, T.A. and Pechinkin, A.V. (2013). Stationary characteristics of the queueing system with LIFO service, probabilistic priority, and hysteric policy, Informatika Primenenia 7(1): 22-35, (in Russian).
Moreno, P. (2006). A discrete-time retrial queue with unreliable server and general service lifetime, Journal of Mathematical Sciences 132(5): 643-655.
Oliver, C.I. and Olubukola, A.I. (2014). M/M/1 multiple vacation queueing systems with differentiated vacations, Modelling and Simulation in Engineering 2014(1): 1-6.
Park, H.M., Yang, W.S. and Chae, K.C. (2009). The Geo/G/1 queue with negative customers and disasters, Stochastic Models 25(4): 673-688.
Pechinkin, A. and Svischeva, T. (2004). The stationary state probability in the BMAP/G/1/r queueing system with inverse discipline and probabilistic priority, 24th International Seminar on Stability Problems for Stochastic Models, Jurmala, Latvia, pp. 141-174.
Piórkowski, A. and Werewka, J. (2010). Minimization of the total completion time for asynchronous transmission in a packet data-transmission system, International Journal of Applied Mathematics and Computer Science 20(2): 391-400, DOI: 10.2478/v10006-010-0029-z.
Takagi, H. (1993). Queueing analysis: A Foundation of Performance Evaluation, Discrete-Time Systems, North-Holland, Amsterdam.
Tian, N. and Zhang, Z. (2002). The discrete-time GI/Geo/1 queue with multiple vacations, Queueing Systems 40(3): 283-294.
Tian, N. and Zhang, Z. (2006). Vacation Queueing Models: Theory and Applications, Springer, New York, NY.
Walraevens, J., Steyaert, B. and Bruneel, H. (2006). A preemptive repeat priority queue with resampling: Performance analysis, Annals of Operations Research 146(1): 189-202.
Wieczorek, R. (2010). Markov chain model of phytoplankton dynamics, International Journal of Applied Mathematics and Computer Science 20(4): 763-771, DOI: 10.2478/v10006-010-0058-7.
Woodward, M.E. (1994). Communication and Computer Networks: Modelling with Discrete-Time Queues, IEEE Computer Society, London.
Xeung, W., Jin, D., Dae, W. and Kyung, C. (2007). The Geo/G/1 queue with disasters and multiple working vacations, Stochastic Models 23(4): 537-549.