Strategic Joining in an M/M/1 Constant Retrial Queue with Reserved Idle Time Under N-Policy

2019 ◽  
pp. 374-388
Author(s):  
Jinting Wang ◽  
Lulu Li
Keyword(s):  
Retrial Queue ◽  
Idle Time

scholarly journals Two-way communication retrial queue with unreliable server and multiple types of outgoing calls

2020 ◽  
Vol 28 (1) ◽  
pp. 49-61
Author(s):  
Anatoly A. Nazarov ◽  
Svetlana V. Paul ◽  
Olga D. Lizyura
Keyword(s):  
Probability Distribution ◽  
Call Center ◽  
Poisson Point Process ◽  
Retrial Queue ◽  
Idle Time ◽  
High Rate ◽  
Exponential Distributions ◽  
Limit Condition ◽  
Different Types ◽  
Incoming Call

Retrial queue under consideration is the model of call center operator switching between input and outgoing calls. Incoming calls form a Poisson point process. Upon arrival, an incoming call occupies the server for an exponentially distributed service time if the server is idle. If the server if busy, an incoming call joins the orbit to make a delay before the next attempt to take the server. The probability distribution of the length of delay is an exponential distribution. Otherwise, the server makes outgoing calls in its idle time. There are multiple types of outgoing calls in the system. Outgoing call rates are different for each type of outgoing call. Durations of different types of outgoing calls follow distinct exponential distributions. Unsteadiness is that the server crashes after an exponentially distributed time and needs recovery. The rates of breakdowns and restorations are different and depend on server state. Our contribution is to obtain the probability distribution of the number of calls in the orbit under high rate of making outgoing calls limit condition. Based on the obtained asymptotics, we have built the approximations of the probability distribution of the number of calls in the orbit.

scholarly journals Heavy outgoing call asymptotics for retrial queue with two way communication and multiple types of outgoing calls

2019 ◽  
Vol 27 (1) ◽  
pp. 5-20
Author(s):  
Anatoly A Nazarov ◽  
Svetlana V Paul ◽  
Olga D Lizyura
Keyword(s):  
Probability Distribution ◽  
Poisson Process ◽  
Service Time ◽  
Retrial Queue ◽  
Idle Time ◽  
Single Server ◽  
Queueing Model ◽  
Exponential Distributions ◽  
Incoming Call

In this paper, we consider a single server queueing model M |M |1|N with two types of calls: incoming calls and outgoing calls, where incoming calls arrive at the server according to a Poisson process. Upon arrival, an incoming call immediately occupies the server if it is idle or joins an orbit if the server is busy. From the orbit, an incoming call retries to occupy the server and behaves the same as a fresh incoming call. The server makes an outgoing calls after an exponentially distributed idle time. It can be interpreted as that outgoing calls arrive at the server according to a Poisson process. There are N types of outgoing calls whose durations follow N distinct exponential distributions. Our contribution is to derive the asymptotics of the number of incoming calls in retrial queue under the conditions of high rates of making outgoing calls and low rates of service time of each type of outgoing calls. Based on the obtained asymptotics, we have built the approximations of the probability distribution of the number of incoming calls in the system.

Two-way communication retrial queue with unreliable server and multiple types of outgoing calls

2020 ◽  
Vol 28 (1) ◽  
pp. 49-61
Author(s):  
Anatoly A. Nazarov ◽  
Svetlana V. Paul ◽  
Olga D. Lizyura
Keyword(s):  
Probability Distribution ◽  
Call Center ◽  
Poisson Point Process ◽  
Retrial Queue ◽  
Idle Time ◽  
High Rate ◽  
Exponential Distributions ◽  
Limit Condition ◽  
Different Types ◽  
Incoming Call

Retrial queue under consideration is the model of call center operator switching between input and outgoing calls. Incoming calls form a Poisson point process. Upon arrival, an incoming call occupies the server for an exponentially distributed service time if the server is idle. If the server if busy, an incoming call joins the orbit to make a delay before the next attempt to take the server. The probability distribution of the length of delay is an exponential distribution. Otherwise, the server makes outgoing calls in its idle time. There are multiple types of outgoing calls in the system. Outgoing call rates are different for each type of outgoing call. Durations of different types of outgoing calls follow distinct exponential distributions. Unsteadiness is that the server crashes after an exponentially distributed time and needs recovery. The rates of breakdowns and restorations are different and depend on server state. Our contribution is to obtain the probability distribution of the number of calls in the orbit under high rate of making outgoing calls limit condition. Based on the obtained asymptotics, we have built the approximations of the probability distribution of the number of calls in the orbit.

Idle time utilization through service to customers in a retrial queue maintaining high system reliability*

2013 ◽  
Vol 191 (4) ◽  
pp. 506-517
Author(s):  
A. N. Dudin ◽  
A. Krishnamoorthy ◽  
V. C. Narayanan
Keyword(s):  
System Reliability ◽  
Retrial Queue ◽  
Idle Time ◽  
High System ◽  
Time Utilization

Two-way communication retrial queue with unreliable server and multiple types of outgoing calls

2020 ◽  
Vol 28 (1) ◽  
pp. 49-61
Author(s):  
Anatoly A. Nazarov ◽  
Svetlana V. Paul ◽  
Olga D. Lizyura
Keyword(s):  
Probability Distribution ◽  
Call Center ◽  
Poisson Point Process ◽  
Retrial Queue ◽  
Idle Time ◽  
High Rate ◽  
Exponential Distributions ◽  
Limit Condition ◽  
Different Types ◽  
Incoming Call

Retrial queue under consideration is the model of call center operator switching between input and outgoing calls. Incoming calls form a Poisson point process. Upon arrival, an incoming call occupies the server for an exponentially distributed service time if the server is idle. If the server if busy, an incoming call joins the orbit to make a delay before the next attempt to take the server. The probability distribution of the length of delay is an exponential distribution. Otherwise, the server makes outgoing calls in its idle time. There are multiple types of outgoing calls in the system. Outgoing call rates are different for each type of outgoing call. Durations of different types of outgoing calls follow distinct exponential distributions. Unsteadiness is that the server crashes after an exponentially distributed time and needs recovery. The rates of breakdowns and restorations are different and depend on server state. Our contribution is to obtain the probability distribution of the number of calls in the orbit under high rate of making outgoing calls limit condition. Based on the obtained asymptotics, we have built the approximations of the probability distribution of the number of calls in the orbit.

Two-echelon imperfect production fuzzy supply chain model for reliability dependent demand with probabilistic deterioration and rework

2021 ◽  
pp. 1-15
Author(s):  
Sudip Adak ◽  
G.S. Mahapatra
Keyword(s):  
Supply Chain ◽  
Production Rate ◽  
Production Cost ◽  
Idle Time ◽  
Chain Model ◽  
Specific Time ◽  
Defective Items ◽  
Imperfect Production ◽  
Supply Chain Model ◽  
Dependent Demand

This paper develops a fuzzy two-layer supply chain for manufacturer and retailer with defective and non-defective types of products. The manufacturer produces up to a specific time, including faulty and non-defective items, and after the screening, the non-defective item sends to the retailer. The retailer’s strategy is to do the screening of items received from the manufacturer; subsequently, the perfect quality items are used to fulfill the customer’s demand, and the defective items are reworked. The retailer considers that customer demand is time and reliability dependent. The supply chain considers probabilistic deterioration for the manufacturer and retailers along with the strategies such as production rate, unit production cost, cost of idle time of manufacturer, screening, rework, etc. The optimum average profit of the integrated model is evaluated for both the cases crisp and fuzzy environments. Managerial insights and the effect of changes in the parameters’ values on the optimal inventory policy under fuzziness are presented.

Sign in / Sign up

Export Citation Format

Share Document