scholarly journals Analysis of a Queueing Model with Batch Markovian Arrival Process and General Distribution for Group Clearance

2020 ◽  
Author(s):  
Srinivas R. Chakravarthy ◽  
Shruti ◽  
Alexander Rumyantsev
Keyword(s):  
Markovian Arrival Process ◽  
Arrival Process ◽  
General Distribution ◽  
Queueing Model ◽  
Batch Markovian Arrival Process

scholarly journals Some performance measures for vacation models with a batch Markovian arrival process

1994 ◽  
Vol 7 (2) ◽  
pp. 111-124 ◽  
Author(s):  
Sadrac K. Matendo
Keyword(s):  
Performance Measures ◽  
Waiting Times ◽  
Distribution Functions ◽  
Markovian Arrival Process ◽  
Arrival Process ◽  
Service Discipline ◽  
Renewal Processes ◽  
Single Server ◽  
Batch Markovian Arrival Process ◽  
Interarrival Times

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 vacation or not, when the system is empty, depends on the number of vacations already taken in the current inactive phase. This exhaustive service discipline includes the single vacation T-policy, T(SV), and the multiple vacation T-policy, T(MV). The service times are i.i.d. random variables, independent of the interarrival times and the vacation durations. Some important performance measures such as the distribution functions and means of the virtual and the actual waiting times are given. Finally, a numerical example is presented.

scholarly journals Elucidating the Short Term Loss Behavior of Markovian-Modulated Batch-Service Queueing Model with Discrete-Time Batch Markovian Arrival Process

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yung-Chung Wang ◽  
Dong-Liang Cai ◽  
Li-Hsin Chiang ◽  
Cheng-Wei Hu
Keyword(s):  
Discrete Time ◽  
Packet Loss ◽  
Loss Probability ◽  
Markovian Arrival Process ◽  
Arrival Process ◽  
Service Process ◽  
Batch Service ◽  
Temporal Behavior ◽  
Packet Loss Probability ◽  
Batch Markovian Arrival Process

This paper applies a matrix-analytical approach to analyze the temporal behavior of Markovian-modulated batch-service queue with discrete-time batch Markovian arrival process (DBMAP). The service process is correlated and its structure is presented through discrete-time batch Markovian service process (DBMSP). We examine the temporal behavior of packet loss by means of conditional statistics with respect to congested and noncongested periods that occur in an alternating manner. The congested period corresponds to having more than a certain number of packets in the buffer; noncongested period corresponds to the opposite. All of the four related performance measures are derived, including probability distributions of a congested and noncongested periods, the probability that the system stays in a congested period, the packet loss probability during congested period, and the long term packet loss probability. Queueing systems of this type arise in the domain of wireless communications.

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