Multiserver Queueing System with Non-homogeneous Customers and Sectorized Memory Space

2018 ◽  
pp. 272-285 ◽  
Author(s):  
Marcin Ziółkowski ◽  
Oleg Tikhonenko
Keyword(s):  
Queueing System ◽  
Memory Space ◽  
Multiserver Queueing System

scholarly journals Analysis of Multiserver Queueing System with Opportunistic Occupation and Reservation of Servers

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Bin Sun ◽  
Moon Ho Lee ◽  
Sergey A. Dudin ◽  
Alexander N. Dudin
Keyword(s):  
System Performance ◽  
Queueing System ◽  
Optimal Choice ◽  
Preemptive Priority ◽  
Rate Dependent ◽  
Service Type ◽  
The Subject ◽  
Multiserver Queueing System

We consider a multiserver queueing system with two input flows. Type-1 customers have preemptive priority and are lost during arrival only if all servers are occupied by type-1 customers. If all servers are occupied, but some provide service to type-2 customers, service of type-2 customer is terminated and type-1 customer occupies the server. If the number of busy servers is less than the thresholdMduring type-2 customer arrival epoch, this customer is accepted. Otherwise, it is lost or becomes a retrial customer. It will retry to obtain service. Type-2 customer whose service is terminated is lost or moves to the pool of retrial customers. The service time is exponentially distributed with the rate dependent on the customer’s type. Such queueing system is suitable for modeling cognitive radio. Type-1 customers are interpreted as requests generated by primary users. Type-2 customers are generated by secondary or cognitive users. The problem of optimal choice of the thresholdMis the subject of this paper. Behavior of the system is described by the multidimensional Markov chain. Its generator, ergodicity condition, and stationary distribution are given. The system performance measures are obtained. The numerical results show the effectiveness of considered admission control.

scholarly journals Sensitivity Analysis and Simulation of a Multiserver Queueing System with Mixed Service Time Distribution

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1277
Author(s):  
Evsey Morozov ◽  
Michele Pagano ◽  
Irina Peshkova ◽  
Alexander Rumyantsev
Keyword(s):  
Service Time ◽  
Queueing System ◽  
Queueing Systems ◽  
Mixture Distribution ◽  
Service Time Distribution ◽  
Perfect Sampling ◽  
Mixing Distributions ◽  
Single Input ◽  
Theoretical Results ◽  
Multiserver Queueing System

The motivation of mixing distributions in communication/queueing systems modeling is that some input data (e.g., service time in queueing models) may follow several distinct distributions in a single input flow. In this paper, we study the sensitivity of performance measures on proximity of the service time distributions of a multiserver system model with two-component Pareto mixture distribution of service times. The theoretical results are illustrated by numerical simulation of the M/G/c systems while using the perfect sampling approach.

scholarly journals MAP+MAP/M2/N/∞Queueing System with Absolute Priority and Reservation of Servers

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Bin Sun ◽  
Moon Ho Lee ◽  
Alexander N. Dudin ◽  
Sergey A. Dudin
Keyword(s):  
Time Distribution ◽  
Queueing System ◽  
Waiting Time Distribution ◽  
Stieltjes Transform ◽  
Absolute Priority ◽  
Arrival Processes ◽  
System States ◽  
Multiserver Queueing System

We consider a multiserver queueing system with an infinite buffer and two types of customers. The flow of customers is described by two Markovian arrival processes (MAPs). Type 1 customers have absolute priority over type 2 customers. If the arriving type 1 customer encounters all servers busy, but some of them provide service to type 2 customers, service of one type 2 customer is terminated and type 1 customer occupies the released server. To avoid too frequent termination of service of type 2 customers, we suggest reservation of some number of servers for type 1 customers. Type 2 customers, who do not succeed to get a server upon arrival or are knocked out from a server, join the buffer or leave the system forever. During a waiting period in the buffer, type 2 customers can be impatient and may leave the system forever. The ergodicity condition of the system is derived in an analytically tractable form. The stationary distribution of the system states and the main performance measures are calculated. The Laplace-Stieltjes transform of the waiting time distribution of an arbitrary type 2 customer is derived. Numerical examples are presented. The problem of the optimal channel reservation is numerically solved.

scholarly journals Queueing System with Heterogeneous Customers as a Model of a Call Center with a Call-Back for Lost Customers

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Sergey Dudin ◽  
Chesoong Kim ◽  
Olga Dudina ◽  
Janghyun Baek
Keyword(s):  
Call Center ◽  
Queueing System ◽  
Optimal Choice ◽  
Arrival Process ◽  
Finite Buffers ◽  
Different Types ◽  
Sojourn Time Distribution ◽  
Multiserver Queueing System

A multiserver queueing system with infinite and finite buffers, two types of customers, and two types of servers as a model of a call center with a call-back for lost customers is investigated. Type 1 customers arrive to the system according to a Markovian arrival process. All rejected type 1 customers become type 2 customers. Typer,r=1,2, servers serve typercustomers if there are any in the system and serve typer′,r′=1,2,  r′≠r,customers if there are no typercustomers in the system. The service times of different types of customers have an exponential distribution with different parameters. The steady-state distribution of the system is analyzed. Some key performance measures are calculated. The Laplace-Stieltjes transform of the sojourn time distribution of type 2 customers is derived. The problem of optimal choice of the number of each type servers is solved numerically.

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