Priority queueing system with many types of requests and restricted processor sharing

D’Apice, Ciro; Dudin, Alexander; Dudin, Sergey; Manzo, Rosanna

doi:10.1007/s12652-022-04233-w

Cited by 13 publications

(4 citation statements)

References 27 publications

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“…storing, finite buffer for demands and retrying of demands, disastrous disappearance of demands or (and) energy, service devices breakdowns, etc. An extension of the model to the controlled priority systems, see, e.g., [52], is planned.…”

Section: Discussionmentioning

confidence: 99%

Optimal Hysteresis Control via a Queuing System with Two Heterogeneous Energy-Consuming Servers

D’Apice,

D’Arienzo,

Dudin

et al. 2023

Mathematics

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A queuing system having two different servers is under study. Demands enter the system according to a Markov arrival process. Service times have phase-type distribution. Service of demands is possible only if the fixed number of energy units, probably different for two servers, is available in the system at the potential service beginning moment. Energy units arrive in the system also according to a Markov arrival process and are stored in a stock (battery) of a finite capacity. Leakage of energy units from the stock can occur. Demands waiting in the infinite buffer are impatient and can leave the buffer after an exponentially distributed waiting time. One server is the main one and permanently provides service when the buffer is not empty and the required number of energy units is available. The second server is the assistant server and is switched on or off depending on the availability of energy units and queue length according to the hysteresis strategy defined by two thresholds. The assistant server is switched on when the queue length is not less than the greater threshold and is switched off when the queue length becomes smaller than the smaller threshold. The use of the assistant server has to be paid. Thus, the problem of the optimal selection of the thresholds defining the control strategy naturally arises. To solve this problem, the study of the behavior of the system under any fixed values of the parameters of the control strategy is necessary. Such a study is given in this paper. Numerical results are presented. They illustrate the feasibility of computer realization of the developed algorithms for computation of the stationary distribution of the system states and the main key performance indicators as well as the result of solving one of the possible optimization tasks.

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Section: Discussionmentioning

confidence: 99%

Optimal Hysteresis Control via a Queuing System with Two Heterogeneous Energy-Consuming Servers

D’Apice,

D’Arienzo,

Dudin

et al. 2023

Mathematics

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“…• We assume MAP flows of both types of users what is essential advantage over the vast majority of existing research, except the papers [10], [12], [14], [32], [38], [39].…”

Section: Contributions Of This Papermentioning

confidence: 99%

“…In particular, these systems are now popular for description of emergency rooms, see, e.g. [1], [18], [21], and cognitive radio networks, see, e.g., surveys [2] and [36] and papers [9], [10],…”

Section: Introductionmentioning

confidence: 99%

Admission Control in Priority Queueing System With Servers Reservation and Temporal Blocking Admission of Low Priority Users

et al. 2023

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We analyse a cell of Cognitive Radio Network (CRN ) as the multiline queueing system supplying service to two Markovian arrival flows of users. Primary (or licensed) users called as High Priority Users (HPU s) have a preemptive priority over the secondary (cognitive) users called as Low Priority Users (LPU s). The HPU s are dropped upon the arrival only if all servers are occupied by HPU s. If at the arrival epoch all servers are busy but some of them provide service to LPU s, service of one LPU is immediately interrupted and service of the HPU begins in the released server. A LPU is accepted only if the number of busy servers at arrival epoch is less than the defined in advance threshold M . Otherwise, the LPU is permanently lost or becomes a retrial user. A retrial user repeats attempts to receive service later after random time intervals. The LPU whose service is interrupted is either lost or transferred to a virtual place called as orbit. The users placed in the orbit may be impatient and can renege the system. The service time follows an exponential probability distribution with the rate determined by the user's type. After loss of a HPU , admission of LPU s is blocked. LPU s are informed that their access is temporarily suspended and do not generate new requests until blocking expires. The purpose of the research is the optimization of threshold M and admission blocking period duration. Behavior of the system is described by a multidimensional continuous-time Markov chain. Its generator, ergodicity condition and invariant distribution are derived. Expressions for performance indicators are given. Numerical results demonstrating usefulness of blocking and significance of account of correlation in arrivals are presented. E.g., in the presented example of cost criterion optimization blocking gives 18 percent profit comparing to the system without blocking.

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“…In D'Apice et al [6], a queueing system is studied with a discipline such that assumes a restriction for the bandwidth (capacity) of the server and the number of jobs that are serviced simultaneously. The jobs can be interrupted by jobs of the higher priorities and preempted jobs are lost.…”

Section: Introductionmentioning

confidence: 99%

Loss probability in priority limited processing queueing system

Yashina

Tatashev

Alencar

2023

Math Methods in App Sciences

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In this paper, a queueing system with a preemptive priority limited processor sharing system with some versions of the discipline is considered. The problem of lost probability is an important aspect for developing methods to improve efficiency and productivity of in modern communications system and computer networks. In the paper, the following conditions are considered. The total service rate depends on the number of jobs serviced simultaneously, and this number is limited. The service rate of simultaneously serviced jobs is the same. There are jobs of different priorities. If the maximum quantity of jobs are serviced simultaneously, and a new job arrives, then depending on the priorities of the arriving and serviced jobs, the arriving job can be lost or preempt a serviced job. Four versions of the service discipline are considered. Depending on the discipline version, an arriving job can preempt or not preempt a job of the same priority, and preempted job is lost or its service is resumed later. This paper develops an approach to compute the loss probability of a prescribed priority job for each version of the discipline.

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Priority queueing system with many types of requests and restricted processor sharing

Cited by 13 publications

References 27 publications

Optimal Hysteresis Control via a Queuing System with Two Heterogeneous Energy-Consuming Servers

Optimal Hysteresis Control via a Queuing System with Two Heterogeneous Energy-Consuming Servers

Admission Control in Priority Queueing System With Servers Reservation and Temporal Blocking Admission of Low Priority Users

Loss probability in priority limited processing queueing system

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