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Journal articles on the topic 'Batch arrival'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Lichtzinder, B. Ya, A. Yu Privalov, and V. I. Moiseev. "Batch poissonian arrival models of multiservice network traffic." Проблемы передачи информации 59, no. 1 (2023): 71–79. http://dx.doi.org/10.31857/s0555292323010060.

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The emergence of packet-switched communication networks has made it clear that Poissonian arrival flow models are not quite adequate and required the development of new models based on non-Poisson distributions. This paper is devoted to the analysis of a particular case of a batch Markovian flow, namely, batch (nonordinary) Poissonian arrivals. Such a flow is stationary and memoryless but not ordinary. We consider a class of queueing systems with constant service time. We present results of analytical computations of arrival flow parameters and also simulation results. We show that the varianc

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2

Van Houdt, B., and C. Blondia. "The delay distribution of a type k customer in a first-come-first-served MMAP[K]/PH[K]/1 queue." Journal of Applied Probability 39, no. 1 (2002): 213–23. http://dx.doi.org/10.1239/jap/1019737998.

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This paper presents an algorithmic procedure to calculate the delay distribution of a type k customer in a first-come-first-served (FCFS) discrete-time queueing system with multiple types of customers, where each type has different service requirements (the MMAP[K]/PH[K]/1 queue). First, we develop a procedure, using matrix analytical methods, to handle arrival processes that do not allow batch arrivals to occur. Next, we show that this technique can be generalized to arrival processes that do allow batch arrivals to occur. We end the paper by presenting some numerical examples.

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Van Houdt, B., and C. Blondia. "The delay distribution of a type k customer in a first-come-first-served MMAP[K]/PH[K]/1 queue." Journal of Applied Probability 39, no. 01 (2002): 213–23. http://dx.doi.org/10.1017/s0021900200021616.

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This paper presents an algorithmic procedure to calculate the delay distribution of a type k customer in a first-come-first-served (FCFS) discrete-time queueing system with multiple types of customers, where each type has different service requirements (the MMAP[K]/PH[K]/1 queue). First, we develop a procedure, using matrix analytical methods, to handle arrival processes that do not allow batch arrivals to occur. Next, we show that this technique can be generalized to arrival processes that do allow batch arrivals to occur. We end the paper by presenting some numerical examples.

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Krishnamoorthy, Achyutha, Anu Nuthan Joshua, and Dmitry Kozyrev. "Analysis of a Batch Arrival, Batch Service Queuing-Inventory System with Processing of Inventory While on Vacation." Mathematics 9, no. 4 (2021): 419. http://dx.doi.org/10.3390/math9040419.

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A single-server queuing-inventory system in which arrivals are governed by a batch Markovian arrival process and successive arrival batch sizes form a finite first-order Markov chain is considered in this paper. Service is provided in batches according to a batch Markovian service process, with consecutive service batch sizes forming a finite first-order Markov chain. A service starts for the next batch on completion of the current service, provided that inventory is available at that epoch; otherwise, there will be a delay in starting the next service. When the service of a batch is completed

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5

Banik, A. D., M. L. Chaudhry, and James J. Kim. "A Note on the Waiting-Time Distribution in an Infinite-Buffer GI[X]/C-MSP/1 Queueing System." Journal of Probability and Statistics 2018 (September 2, 2018): 1–10. http://dx.doi.org/10.1155/2018/7462439.

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This paper deals with a batch arrival infinite-buffer single server queue. The interbatch arrival times are generally distributed and arrivals are occurring in batches of random size. The service process is correlated and its structure is presented through a continuous-time Markovian service process (C-MSP). We obtain the probability density function (p.d.f.) of actual waiting time for the first and an arbitrary customer of an arrival batch. The proposed analysis is based on the roots of the characteristic equations involved in the Laplace-Stieltjes transform (LST) of waiting times in the syst

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Pang, Guodong, and Ward Whitt. "INFINITE-SERVER QUEUES WITH BATCH ARRIVALS AND DEPENDENT SERVICE TIMES." Probability in the Engineering and Informational Sciences 26, no. 2 (2012): 197–220. http://dx.doi.org/10.1017/s0269964811000337.

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Motivated by large-scale service systems, we consider an infinite-server queue with batch arrivals, where the service times are dependent within each batch. We allow the arrival rate of batches to be time varying as well as constant. As regularity conditions, we require that the batch sizes be i.i.d. and independent of the arrival process of batches, and we require that the service times within different batches be independent. We exploit a recently established heavy-traffic limit for the number of busy servers to determine the performance impact of the dependence among the service times. The

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Chydzinski, Andrzej. "Burst ratio for a versatile traffic model." PLOS ONE 17, no. 8 (2022): e0272263. http://dx.doi.org/10.1371/journal.pone.0272263.

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We deal with a finite-buffer queue, in which arriving jobs are subject to loss due to buffer overflows. The burst ratio parameter, which reflects the tendency of losses to form long series, is studied in detail. Perhaps the most versatile model of the arrival stream is used, i.e. the batch Markovian arrival process (BMAP). Among other things, it enables modeling the interarrival time density function, the interarrival time autocorrelation function and batch arrivals. The main contribution in an exact formula for the burst ratio in a queue with BMAP arrivals and arbitrary service time distribut

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8

Chydzinski, Andrzej. "Buffer overflow period in a batch-arrival queue with autocorrelated arrivals." Applied Mathematics & Information Sciences 7, no. 4 (2013): 1633–41. http://dx.doi.org/10.12785/amis/070450.

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Chao, Xiuli, Qi-Ming He, and Sheldon Ross. "Tollbooth tandem queues with infinite homogeneous servers." Journal of Applied Probability 52, no. 4 (2015): 941–61. http://dx.doi.org/10.1239/jap/1450802745.

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In this paper we analyze a tollbooth tandem queueing problem with an infinite number of servers. A customer starts service immediately upon arrival but cannot leave the system before all customers who arrived before him/her have left, i.e. customers depart the system in the same order as they arrive. Distributions of the total number of customers in the system, the number of departure-delayed customers in the system, and the number of customers in service at time t are obtained in closed form. Distributions of the sojourn times and departure delays of customers are also obtained explicitly. Bo

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Chao, Xiuli, Qi-Ming He, and Sheldon Ross. "Tollbooth tandem queues with infinite homogeneous servers." Journal of Applied Probability 52, no. 04 (2015): 941–61. http://dx.doi.org/10.1017/s0021900200113002.

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In this paper we analyze a tollbooth tandem queueing problem with an infinite number of servers. A customer starts service immediately upon arrival but cannot leave the system before all customers who arrived before him/her have left, i.e. customers depart the system in the same order as they arrive. Distributions of the total number of customers in the system, the number of departure-delayed customers in the system, and the number of customers in service at time t are obtained in closed form. Distributions of the sojourn times and departure delays of customers are also obtained explicitly. Bo

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11

Cao, Jianyu, and Weixin Xie. "Joint arrival process of multiple independent batch Markovian arrival processes." Statistics & Probability Letters 133 (February 2018): 42–49. http://dx.doi.org/10.1016/j.spl.2017.09.012.

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Chydzinski, Andrzej, and Blazej Adamczyk. "Transient and Stationary Losses in a Finite-Buffer Queue with Batch Arrivals." Mathematical Problems in Engineering 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/326830.

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We present an analysis of the number of losses, caused by the buffer overflows, in a finite-buffer queue with batch arrivals and autocorrelated interarrival times. Using the batch Markovian arrival process, the formulas for the average number of losses in a finite time interval and the stationary loss ratio are shown. In addition, several numerical examples are presented, including illustrations of the dependence of the number of losses on the average batch size, buffer size, system load, autocorrelation structure, and time.

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Li, Bo, and Guodong Pang. "Shot noise processes with randomly delayed cluster arrivals and dependent noises in the large-intensity regime." Advances in Applied Probability 53, no. 4 (2021): 1190–221. http://dx.doi.org/10.1017/apr.2021.16.

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AbstractWe study shot noise processes with cluster arrivals, in which entities in each cluster may experience random delays (possibly correlated), and noises within each cluster may be correlated. We prove functional limit theorems for the process in the large-intensity asymptotic regime, where the arrival rate gets large while the shot shape function, cluster sizes, delays, and noises are unscaled. In the functional central limit theorem, the limit process is a continuous Gaussian process (assuming the arrival process satisfies a functional central limit theorem with a Brownian motion limit).

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Lee, Moon Ho, and Sergey A. Dudin. "An Erlang Loss Queue with Time-Phased Batch Arrivals as a Model for Traffic Control in Communication Networks." Mathematical Problems in Engineering 2008 (2008): 1–14. http://dx.doi.org/10.1155/2008/814740.

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A multiserver queueing model that does not have a buffer but has batch arrival of customers is considered. In contrast to the standard batch arrival, in which the entire batch arrives at the system during a single epoch, we assume that the customers of a batch (flow) arrive individually in exponentially distributed times. The service time is exponentially distributed. Flows arrive according to a stationary Poisson arrival process. The flow size distribution is geometric. The number of flows that can be simultaneously admitted to the system is under control. The loss of any customer from an adm

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15

Chao, Xiuli. "Partial balances in batch arrival batch service and assemble-transfer queueing networks." Journal of Applied Probability 34, no. 3 (1997): 745–52. http://dx.doi.org/10.2307/3215099.

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Recently Miyazawa and Taylor (1997) proposed a new class of queueing networks with batch arrival batch service and assemble-transfer features. In such networks customers arrive and are served in batches, and may change size when a batch transfers from one node to another. With the assumption of an additional arrival process at each node when it is empty, they obtain a simple product-form steady-state probability distribution, which is a (stochastic) upper bound for the original network. This paper shows that this class of network possesses a set of non-standard partial balance equations, and i

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Chao, Xiuli. "Partial balances in batch arrival batch service and assemble-transfer queueing networks." Journal of Applied Probability 34, no. 03 (1997): 745–52. http://dx.doi.org/10.1017/s0021900200101391.

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Recently Miyazawa and Taylor (1997) proposed a new class of queueing networks with batch arrival batch service and assemble-transfer features. In such networks customers arrive and are served in batches, and may change size when a batch transfers from one node to another. With the assumption of an additional arrival process at each node when it is empty, they obtain a simple product-form steady-state probability distribution, which is a (stochastic) upper bound for the original network. This paper shows that this class of network possesses a set of non-standard partial balance equations, and i

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17

Borovkov, A. A., and R. Schassberger. "Ergodicity of a Jackson network by batch arrivals." Journal of Applied Probability 31, no. 3 (1994): 847–53. http://dx.doi.org/10.2307/3215163.

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The Jackson network under study receives batch arrivals at i.i.d. intervals and features Markovian routing and exponentially distributed service times. The system is shown to be stable, in the sense of not being overloaded, if and only if, for each node, the total arrival rate of external and internal customers is less than the service rate. The method of proof is of more general interest.

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Borovkov, A. A., and R. Schassberger. "Ergodicity of a Jackson network by batch arrivals." Journal of Applied Probability 31, no. 03 (1994): 847–53. http://dx.doi.org/10.1017/s0021900200045411.

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The Jackson network under study receives batch arrivals at i.i.d. intervals and features Markovian routing and exponentially distributed service times. The system is shown to be stable, in the sense of not being overloaded, if and only if, for each node, the total arrival rate of external and internal customers is less than the service rate. The method of proof is of more general interest.

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19

Peköz, Erol A., Rhonda Righter, and Cathy H. Xia. "Characterizing losses during busy periods in finite buffer systems." Journal of Applied Probability 40, no. 1 (2003): 242–49. http://dx.doi.org/10.1239/jap/1044476837.

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For multiple-server finite-buffer systems with batch Poisson arrivals, we explore how the distribution of the number of losses during a busy period changes with the buffer size and the initial number of customers. We show that when the arrival rate equals the maximal service rate (ρ= 1), as the buffer size increases the number of losses in a busy period increases in the convex sense, and whenρ> 1, as the buffer size increases the number of busy period losses increases in the increasing convex sense. Also, the number of busy period losses is stochastically increasing in the initial number of

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Peköz, Erol A., Rhonda Righter, and Cathy H. Xia. "Characterizing losses during busy periods in finite buffer systems." Journal of Applied Probability 40, no. 01 (2003): 242–49. http://dx.doi.org/10.1017/s0021900200022361.

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For multiple-server finite-buffer systems with batch Poisson arrivals, we explore how the distribution of the number of losses during a busy period changes with the buffer size and the initial number of customers. We show that when the arrival rate equals the maximal service rate (ρ = 1), as the buffer size increases the number of losses in a busy period increases in the convex sense, and when ρ &gt; 1, as the buffer size increases the number of busy period losses increases in the increasing convex sense. Also, the number of busy period losses is stochastically increasing in the initial nu

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21

Lev, Raskin, Sira Oksana, Palant Oleksii, and Vodovozov Yevgeniy. "DEVELOPMENT OF A MODEL OF THE SERVICE SYSTEM OF BATCH ARRIVALS IN THE PASSENGERS FLOW OF PUBLIC TRANSPORT." Eastern-European Journal of Enterprise Technologies 5, no. 3 (101) (2019): 51–56. https://doi.org/10.15587/1729-4061.2019.180562.

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A mathematical model of the queuing system for the passenger flow of urban public transport is proposed. The resulting model differs from canonical models of queuing theory by taking into account the fundamental features of real systems. Firstly, the service process is divided into different successive service sessions. Secondly, arrival and departures are batch. Thirdly, the arrival rates vary in different service sessions. Fourthly, the laws of distribution of the number of jobs in batch arrivals for different sessions are different. Fifth, the laws of distribution of the number of batch arr

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22

Henderson, W., and P. G. Taylor. "Some new results on queueing networks with batch movement." Journal of Applied Probability 28, no. 2 (1991): 409–21. http://dx.doi.org/10.2307/3214876.

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Product-form equilibrium distributions in networks of queues in which customers move singly have been known since 1957, when Jackson derived some surprising independence results. A product-form equilibrium distribution has also recently been shown to be valid for certain queueing networks with batch arrivals, batch services and even correlated routing.This paper derives the joint equilibrium distribution of states immediately before and after a batch of customers is released into the network. The results are valid for either discrete- or continuous-time queueing networks: previously obtained r

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23

Henderson, W., and P. G. Taylor. "Some new results on queueing networks with batch movement." Journal of Applied Probability 28, no. 02 (1991): 409–21. http://dx.doi.org/10.1017/s0021900200039784.

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Product-form equilibrium distributions in networks of queues in which customers move singly have been known since 1957, when Jackson derived some surprising independence results. A product-form equilibrium distribution has also recently been shown to be valid for certain queueing networks with batch arrivals, batch services and even correlated routing. This paper derives the joint equilibrium distribution of states immediately before and after a batch of customers is released into the network. The results are valid for either discrete- or continuous-time queueing networks: previously obtained

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Miyazawa, Masakiyo, and Peter G. Taylor. "A Geometric Product-Form Distribution for a Queueing Network by Non-Standard Batch Arrivals and Batch Transfers." Advances in Applied Probability 29, no. 2 (1997): 523–44. http://dx.doi.org/10.2307/1428015.

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We introduce a batch service discipline, called assemble-transfer batch service, for continuous-time open queueing networks with batch movements. Under this service discipline a requested number of customers is simultaneously served at a node, and transferred to another node as, possibly, a batch of different size, if there are sufficient customers there; the node is emptied otherwise. We assume a Markovian setting for the arrival process, service times and routing, where batch sizes are generally distributed.Under the assumption that extra batches arrive while nodes are empty, and under a sta

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Miyazawa, Masakiyo, and Peter G. Taylor. "A Geometric Product-Form Distribution for a Queueing Network by Non-Standard Batch Arrivals and Batch Transfers." Advances in Applied Probability 29, no. 02 (1997): 523–44. http://dx.doi.org/10.1017/s0001867800028111.

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We introduce a batch service discipline, called assemble-transfer batch service, for continuous-time open queueing networks with batch movements. Under this service discipline a requested number of customers is simultaneously served at a node, and transferred to another node as, possibly, a batch of different size, if there are sufficient customers there; the node is emptied otherwise. We assume a Markovian setting for the arrival process, service times and routing, where batch sizes are generally distributed. Under the assumption that extra batches arrive while nodes are empty, and under a st

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Matendo, Sadrac K. "Some performance measures for vacation models with a batch Markovian arrival process." Journal of Applied Mathematics and Stochastic Analysis 7, no. 2 (1994): 111–24. http://dx.doi.org/10.1155/s1048953394000134.

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We consider a single server infinite capacity queueing system, where the arrival process is a batch Markovian arrival process (BMAP). Particular BMAPs are the batch Poisson arrival process, the Markovian arrival process (MAP), many batch arrival processes with correlated interarrival times and batch sizes, and superpositions of these processes. We note that the MAP includes phase-type (PH) renewal processes and non-renewal processes such as the Markov modulated Poisson process (MMPP).The server applies Kella's vacation scheme, i.e., a vacation policy where the decision of whether to take a new

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Hordijk, Arie, and Ger Koole. "On the Optimality of the Generalized Shortest Queue Policy." Probability in the Engineering and Informational Sciences 4, no. 4 (1990): 477–87. http://dx.doi.org/10.1017/s0269964800001777.

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Consider a queueing model in which arriving customers have to choose between m parallel servers, each with its own queue. We prove for general arrival streams that the policy which assigns to the shortest queue is stochastically optimal for models with finite buffers and batch arrivals.

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Falin, G. I. "On a multiclass batch arrival retrial queue." Advances in Applied Probability 20, no. 2 (1988): 483–87. http://dx.doi.org/10.2307/1427403.

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Kulkarni (1986) derived expressions for the expected waiting times for customers of two types who arrive in batches at a single-channel repeated orders queueing system. We propose another method of solving this problem and extend Kulkarni&s result to the case of N≧2 classes of customers.

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Falin, G. I. "On a multiclass batch arrival retrial queue." Advances in Applied Probability 20, no. 02 (1988): 483–87. http://dx.doi.org/10.1017/s0001867800017109.

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Kulkarni (1986) derived expressions for the expected waiting times for customers of two types who arrive in batches at a single-channel repeated orders queueing system. We propose another method of solving this problem and extend Kulkarni&amp;s result to the case of N≧2 classes of customers.

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Franx, Geert Jan. "THE MX/D/c BATCH ARRIVAL QUEUE." Probability in the Engineering and Informational Sciences 19, no. 3 (2005): 345–49. http://dx.doi.org/10.1017/s0269964805050199.

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A surprisingly simple and explicit expression for the waiting time distribution of the MX/D/c batch arrival queue is derived by a full probabilistic analysis, requiring neither generating functions nor Laplace transforms. Unlike the solutions known so far, this expression presents no numerical complications, not even for high traffic intensities.

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31

Liu, L., and J. G. C. Templeton. "Autocorrelations in infinite server batch arrival queues." Queueing Systems 14, no. 3-4 (1993): 313–37. http://dx.doi.org/10.1007/bf01158871.

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32

Kim, Bara, and Jeongsim Kim. "A batch arrival queue with impatient customers." Operations Research Letters 42, no. 2 (2014): 180–85. http://dx.doi.org/10.1016/j.orl.2014.02.001.

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Mandjes, Michel. "Rare event analysis of batch-arrival queues." Telecommunication Systems 6, no. 1 (1996): 161–80. http://dx.doi.org/10.1007/bf02114292.

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Seenivasan, M., and K. S.Subasri. "Batch Arrival Queueing Model with Unreliable Server." International Journal of Engineering & Technology 7, no. 4.10 (2018): 269. http://dx.doi.org/10.14419/ijet.v7i4.10.20910.

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The unreliable server with provision of temporary server in the context of application has been investigated. A temporary server is installed when the primary server is over loaded i.e., a ﬁxed queue length of K-policy customers including the customer with the primary server has been build up. The primary server may breakdown while rendering service to the customers; it is sent for the repair. This type of queuing system has been investigated using Matrix Geometric Method to obtain the probabilities of the system steady state.AMS subject classiﬁcation number— 60K25, 60K30 and 90B22.

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Ho Woo Lee and Soon Seok Lee. "A batch arrival queue with different vacations." Computers & Operations Research 18, no. 1 (1991): 51–58. http://dx.doi.org/10.1016/0305-0548(91)90041-o.

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Dudin, Alexander, Sergey Dudin, Rosanna Manzo, and Luigi Rarità. "Queueing system with batch arrival of heterogeneous orders, flexible limited processor sharing and dynamical change of priorities." AIMS Mathematics 9, no. 5 (2024): 12144–69. http://dx.doi.org/10.3934/math.2024593.

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<abstract><p>A queueing system with the discipline of flexible limited sharing of the server is considered. This discipline assumes the admission, for a simultaneous service, of only a finite number of orders, as well as the use of a reduced service rate when the bandwidth required by the admitted orders is less than the total bandwidth of the server. The orders arrive following a batch-marked Markov arrival process, which is a generalization of the well-known $ MAP $ (Markov arrival process) to the cases of heterogeneous orders and batch arrivals. The orders of different types hav

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Foss, Sergey, and Masakiyo Miyazawa. "Two-node fluid network with a heavy-tailed random input: the strong stability case." Journal of Applied Probability 51, A (2014): 249–65. http://dx.doi.org/10.1239/jap/1417528479.

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We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of a two-dimensional workload process. Tail asymptotics have been well studied for two-dimensional reflecting processes where jumps have either a bounded or an unbounded light-tailed distribution. However, the presence of heavy tails totally changes these asymptotics. Here we focus on the case of strong stability where both nodes release fluid at sufficiently high speeds to minimise their mutual influence. We show

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Foss, Sergey, and Masakiyo Miyazawa. "Two-node fluid network with a heavy-tailed random input: the strong stability case." Journal of Applied Probability 51, A (2014): 249–65. http://dx.doi.org/10.1017/s0021900200021318.

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We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of a two-dimensional workload process. Tail asymptotics have been well studied for two-dimensional reflecting processes where jumps have either a bounded or an unbounded light-tailed distribution. However, the presence of heavy tails totally changes these asymptotics. Here we focus on the case of strong stability where both nodes release fluid at sufficiently high speeds to minimise their mutual influence. We show

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Varma, P. Mahendra, Rajyalakshmi Kottapalli, and V. N. Rama Devi. "Finite MX/M/C Queue with State Dependent Service, Two-Class Arrivals and Impatient Customers." Indian Journal Of Science And Technology 17, no. 28 (2024): 2897–902. http://dx.doi.org/10.17485/ijst/v17i28.1611.

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Objectives: 1. To compute the transition probabilities for the queueing system to be in different states. 2. To calculate the average system length and mean waiting time under the specified parameters. 3. To investigate and test the impact of system characteristics on the anticipated system length as well as mean waiting times. Method: MATLAB software is used for the Runge-Kutta method to calculate probabilities and system constants. Findings: An increase in Type-I arrival rate λ1 and Type-II arrival rate λ2 will cause both mean waiting times and queue length to increase, and they are reduced

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Vanitha, D. Veera, and M. Sabrigiriraj. "Analysis of Hybrid Buffering and Retransmission in OBS Networks." Scientific World Journal 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/159245.

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Burst contention is a major problem in the Optical Burst Switching (OBS) networks. Due to inadequate contention resolution techniques, the burst loss is prominent in OBS. In order to resolve contention fiber delay lines, wavelength converters, deflection routing, burst segmentation, and retransmission are used. Each one has its own limitations. In this paper, a new hybrid scheme is proposed which combines buffering and retransmission, which increases the mean number of bursts processed in the system. In this hybrid method, retransmission with controllable arrival and uncontrollable arrival is

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Pradhan, S., U. C. Gupta, and S. K. Samanta. "Analyzing an infinite buffer batch arrival and batch service queue under batch-size-dependent service policy." Journal of the Korean Statistical Society 45, no. 1 (2016): 137–48. http://dx.doi.org/10.1016/j.jkss.2015.08.004.

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Nishimura, Shoichi, and Hajime Sato. "EIGENVALUE EXPRESSION FOR A BATCH MARKOVIAN ARRIVAL PROCESS." Journal of the Operations Research Society of Japan 40, no. 1 (1997): 122–32. http://dx.doi.org/10.15807/jorsj.40.122.

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K. Vijaya. "The Markovian Batch Arrival Queue with Differentiated Vacation." Communications on Applied Nonlinear Analysis 31, no. 3s (2024): 197–211. http://dx.doi.org/10.52783/cana.v31.759.

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A Poisson Batch Arrival Queueing Model with a single server taking two different vacations at various rates is being considered for the study. The probability generating function method of the different states is considered for deriving the various performance measures of the states; numerical cases and cost studies are also extended.

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Boukir, L., L. Bouallouche-Medjkoune, and D. Aïssani. "Strong Stability of the Batch Arrival Queueing Systems." Stochastic Analysis and Applications 28, no. 1 (2009): 8–25. http://dx.doi.org/10.1080/07362990903417904.

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Samikannu, Rita, Ganesan V, and Sundar Rajan Balasubramanian. "Batch Arrival Poisson Queue with Breakdown and Repairs." International Journal of Mathematics in Operational Research 1, no. 1 (2020): 1. http://dx.doi.org/10.1504/ijmor.2020.10024994.

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Rajan, Balasubramanian Sundar, V. Ganesan, and Samikannu Rita. "Batch arrival Poisson queue with breakdown and repairs." International Journal of Mathematics in Operational Research 17, no. 3 (2020): 424. http://dx.doi.org/10.1504/ijmor.2020.110033.

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Hur, Sun, and Suneung Ahn. "Batch arrival queues with vacations and server setup." Applied Mathematical Modelling 29, no. 12 (2005): 1164–81. http://dx.doi.org/10.1016/j.apm.2005.03.002.

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Lee, Euiwoong, and Sahil Singla. "Maximum Matching in the Online Batch-arrival Model." ACM Transactions on Algorithms 16, no. 4 (2020): 1–31. http://dx.doi.org/10.1145/3399676.

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Jin, Fang, Chengxun Wu, and Hui Ou. "Compound Binomial Model with Batch Markovian Arrival Process." Mathematical Problems in Engineering 2020 (November 28, 2020): 1–10. http://dx.doi.org/10.1155/2020/1932704.

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Abstract:

A compound binomial model with batch Markovian arrival process was studied, and the specific definitions are introduced. We discussed the problem of ruin probabilities. Specially, the recursion formulas of the conditional finite-time ruin probability are obtained and the numerical algorithm of the conditional finite-time nonruin probability is proposed. We also discuss research on the compound binomial model with batch Markovian arrival process and threshold dividend. Recursion formulas of the Gerber–Shiu function and the first discounted dividend value are provided, and the expressions of the

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Chydzinski, Andrzej. "Buffer overflow calculations in a batch arrival queue." ACM SIGMETRICS Performance Evaluation Review 34, no. 2 (2006): 19–21. http://dx.doi.org/10.1145/1168134.1168144.

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