A Multiserver Queueing System with Impatient Customers

1999 ◽  
Vol 45 (3) ◽  
pp. 444-448 ◽  
Author(s):  
Nam Kyoo Boots ◽  
Henk Tijms
Keyword(s):  
Queueing System ◽  
Impatient Customers ◽  
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 A Priority Queue with Many Customer Types, Correlated Arrivals and Changing Priorities

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1292
Author(s):  
Seokjun Lee ◽  
Sergei Dudin ◽  
Olga Dudina ◽  
Chesoong Kim ◽  
Valentina Klimenok
Keyword(s):  
Markov Chain ◽  
Waiting Time ◽  
Performance Indicators ◽  
Queueing System ◽  
Priority Queue ◽  
First Aid ◽  
Single Server ◽  
Finite Buffer ◽  
Impatient Customers ◽  
Arrival Times

A single-server queueing system with a finite buffer, several types of impatient customers, and non-preemptive priorities is analyzed. The initial priority of a customer can increase during its waiting time in the queue. The behavior of the system is described by a multi-dimensional Markov chain. The generator of this chain, having essential dependencies between the components, is derived and formulas for computation of the most important performance indicators of the system are presented. The dependence of some of these indicators on the capacity of the buffer space is illustrated. The profound effect of the phenomenon of correlation of successive inter-arrival times and variance of the service time is numerically demonstrated. Results can be used for the optimization of dispatching various types of customers in information transmission systems, emergency departments and first aid stations, perishable foods supply chains, etc.

scholarly journals An inventory system for perishable commodities with random lifetime

1985 ◽  
Vol 17 (1) ◽  
pp. 234-236 ◽  
Author(s):  
David Perry
Keyword(s):  
Queueing System ◽  
Random Variable ◽  
Inventory System ◽  
Impatient Customers

In this study we assume an inventory system for perishable commodities in which the lifetimes of the items stored are i.i.d. random variable with finite mean.We utilize the analogy between this inventory system and a queueing system with impatient customers, to study the process of the lost demand, the death of the unused items and the number of items in the system.

A queueing system with impatient customers

1985 ◽  
Vol 22 (3) ◽  
pp. 688-696 ◽  
Author(s):  
A. G. De Kok ◽  
H. C. Tijms
Keyword(s):  
Performance Measures ◽  
Queueing System ◽  
Fixed Time ◽  
Single Server ◽  
Impatient Customers ◽  
Average Delay ◽  
Practical Applications ◽  
Poisson Input ◽  
General Service Times ◽  
General Service

A queueing situation often encountered in practice is that in which customers wait for service for a limited time only and leave the system if not served during that time. This paper considers a single-server queueing system with Poisson input and general service times, where a customer becomes a lost customer when his service has not begun within a fixed time after his arrival. For performance measures like the fraction of customers who are lost and the average delay in queue of a customer we obtain exact and approximate results that are useful for practical applications.

scholarly journals On a bulk queueing system with impatient customers

1998 ◽  
Vol 3 (6) ◽  
pp. 539-554 ◽  
Author(s):  
Lotfi Tadj ◽  
Lakdere Benkherouf ◽  
Lakhdar Aggoun
Keyword(s):  
Steady State ◽  
Queue Length ◽  
Queueing System ◽  
Impatient Customers ◽  
Ergodicity Condition ◽  
Bulk Service ◽  
Bulk Arrival ◽  
Steady State Probabilities ◽  
System Characteristics

We consider a bulk arrival, bulk service queueing system. Customers are served in batches ofrunits if the queue length is not less thanr. Otherwise, the server delays the service until the number of units in the queue reaches or exceeds levelr. We assume that unserved customers may get impatient and leave the system. An ergodicity condition and steady-state probabilities are derived. Various system characteristics are also computed.

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