<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>M</mml:mi><mml:mi>A</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>M</mml:mi><mml:mi>A</mml:mi><mml:mi>P</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:mi>N</mml:mi><mml:mo>/</mml:mo><mml:mi>∞</mml:mi></mml:math>Queueing System with Absolute Priority and Reservation of Servers

Sun, Bin; Lee, Moon Ho; Dudin, Alexander; Dudin, Sergey

doi:10.1155/2014/813150

Cited by 7 publications

(1 citation statement)

References 41 publications

(62 reference statements)

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“…He and Li [17] obtained stability conditions for a single-server preemptive repeat PQM by assuming MMAP arrival and general distributed service times for distinct classes of customers. Sun et al [27] presented a MAP + MAP/M2/S queueing model with infinite buffer considering the preemptive repeat priority policy and reservation policy. The consideration of exponential distribution for service times restricts the applicability of the model in real life scenario.…”

Section: Introductionmentioning

confidence: 99%

Optimization of traffic control in MMAP[2]/PH[2]/S priority queueing model with PH retrial times and preemptive repeat policy

Raj,

Jain

2021

Preprint

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The presented study elaborates a multi-server priority queueing model considering the preemptive repeat policy and phase-type distribution (PH) for retrial process. The incoming heterogeneous calls are categorized as handoff calls and new calls. The arrival and service processes of both types of calls follow marked Markoian arrival process (MMAP) and PH distribution with distinct parameters, respectively. An arriving new call will be blocked when all the channels are occupied, and consequently will join the orbit (virtual space) of infinite capacity to retry following PH distribution. When all the channels are occupied and a handoff call arrives at the system, out of the following two scenarios, one might take place. In the first scenario, if all the channels are occupied with handoff calls, the arriving handoff call will be lost from the system. While in the second one, if all the channels are occupied and at least one of them is serving a new call, the arriving handoff call will be provided service by using preemptive priority over that new call and the preempted new call will join the orbit. Behaviour of the proposed system is modelled by the level dependent quasi-birth-death (LDQBD) process.The expressions of various performance measures have been derived for the numerical illustration. An optimization problem for optimal channel allocation and traffic control has been formulated and dealt by employing appropriate heuristic approaches.

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Section: Introductionmentioning

confidence: 99%

Optimization of traffic control in MMAP[2]/PH[2]/S priority queueing model with PH retrial times and preemptive repeat policy

Raj,

Jain

2021

Preprint

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Analysis of a priority queueing system with the enhanced fairness of servers scheduling

Lee

Dudin

Dudina

et al. 2022

J Ambient Intell Human Comput

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A multi-server queueing system with two types of customers is analyzed. Both types of customers have own reserved servers and also there is a pool of servers that can be used by both types of customers. Type 1 customers have almost preemptive priority with flexible use of a priority depending on the current number of customers of this type in an infinite buffer. Type 2 customers do not have an input buffer and are lost in cases of absence of available servers upon arrival or expelling (forced termination) from service by Type 1 customers. A multi-dimensional Markov chain, which defines the dynamics of the considered system under the fixed total number of servers, numbers of reserved servers, a pattern of the correlated arriving processes, service rates, and the thresholds defining the mechanism of expelling Type 2 customers from service, is analyzed. A numerical example of solving an optimization problem based on the obtained results is considered. Results can be used for the elaboration of enhanced protocols of servers scheduling in many real-world systems including cognitive radio networks with channels leasing.

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