Stationary increments in the accumulated work process in processor-sharing queues

1989 ◽  
Vol 26 (3) ◽  
pp. 671-677 ◽  
Author(s):  
R. D. Foley ◽  
Georgia-Ann Klutke
Keyword(s):  
Processing Time ◽  
Response Times ◽  
Processor Sharing ◽  
Work Process ◽  
Conditional Response ◽  
New Approach ◽  
Stationary Increments ◽  
Processor Sharing Queues

We present a new approach to the processor-sharing queue that allows us to study the accumulated work process of a job that requires an amount of processing time x. Our approach simplifies the proofs of some earlier results on expected conditional response times and extends them to the M/G/φ (·) class. The approach illuminates some of the paradoxical features of these systems.

Stationary increments in the accumulated work process in processor-sharing queues

1989 ◽  
Vol 26 (03) ◽  
pp. 671-677 ◽  
Author(s):  
R. D. Foley ◽  
Georgia-Ann Klutke
Keyword(s):  
Processing Time ◽  
Response Times ◽  
Processor Sharing ◽  
Work Process ◽  
Conditional Response ◽  
New Approach ◽  
Stationary Increments ◽  
Processor Sharing Queues

We present a new approach to the processor-sharing queue that allows us to study the accumulated work process of a job that requires an amount of processing time x. Our approach simplifies the proofs of some earlier results on expected conditional response times and extends them to the M/G/φ (·) class. The approach illuminates some of the paradoxical features of these systems.

Conditional response times in the M/G/1 processor-sharing system

1983 ◽  
Vol 20 (4) ◽  
pp. 910-915 ◽  
Author(s):  
B. K. Asare ◽  
F. G. Foster
Keyword(s):  
Response Time ◽  
Processing Time ◽  
Response Times ◽  
Processor Sharing ◽  
Conditional Response

The expected response time of a job that requires processing time t and meets n jobs on arrival in the M/G/1 processor-sharing system is derived.

Conditional response times in the M/G/1 processor-sharing system

1983 ◽  
Vol 20 (04) ◽  
pp. 910-915 ◽  
Author(s):  
B. K. Asare ◽  
F. G. Foster
Keyword(s):  
Response Time ◽  
Processing Time ◽  
Response Times ◽  
Processor Sharing ◽  
Conditional Response

The expected response time of a job that requires processing time t and meets n jobs on arrival in the M/G/1 processor-sharing system is derived.

On a relationship between processor-sharing queues and Crump–Mode–Jagers branching processes

1992 ◽  
Vol 24 (3) ◽  
pp. 653-698 ◽  
Author(s):  
Sergei Grishechkin
Keyword(s):  
Processing Time ◽  
Branching Processes ◽  
Heavy Traffic ◽  
Processor Sharing ◽  
Batch Arrivals ◽  
Processor Sharing Queues ◽  
Residual Processing

The M/G/1 queue with batch arrivals and a queueing discipline which is a generalization of processor sharing is studied by means of Crump–Mode–Jagers branching processes. A number of theorems are proved, including investigation of heavy traffic and overloaded queues. Most of the results obtained are also new for the M/G/1 queue with processor sharing. By use of a limiting procedure we also derive new results concerning M/G/1 queues with shortest residual processing time discipline.

On a relationship between processor-sharing queues and Crump–Mode–Jagers branching processes

1992 ◽  
Vol 24 (03) ◽  
pp. 653-698
Author(s):  
Sergei Grishechkin
Keyword(s):  
Processing Time ◽  
Branching Processes ◽  
Heavy Traffic ◽  
Processor Sharing ◽  
Batch Arrivals ◽  
Processor Sharing Queues ◽  
Residual Processing

The M/G/1 queue with batch arrivals and a queueing discipline which is a generalization of processor sharing is studied by means of Crump–Mode–Jagers branching processes. A number of theorems are proved, including investigation of heavy traffic and overloaded queues. Most of the results obtained are also new for the M/G/1 queue with processor sharing. By use of a limiting procedure we also derive new results concerning M/G/1 queues with shortest residual processing time discipline.

scholarly journals Conditional Sojourn times and the volatility of payment schemes for bandwidth sharing in packet networks

2015 ◽  
Vol 52 (04) ◽  
pp. 962-980 ◽  
Author(s):  
Fabrice M. Guillemin ◽  
Ravi R. Mazumdar
Keyword(s):  
Asymptotic Behavior ◽  
Orthogonal Polynomials ◽  
Response Times ◽  
Point Of View ◽  
Packet Networks ◽  
Processor Sharing ◽  
Bandwidth Sharing ◽  
Conditional Response ◽  
Payment Schemes ◽  
Groves Mechanism

Predictability of revenue and costs to both operators and users is critical for payment schemes. We study the issue of the design of payment schemes in networks with bandwidth sharing. The model we consider is a processor sharing system that is accessed by various classes of users with different processing requirements or file sizes. The users are charged according to a Vickrey–Clarke–Groves mechanism because of its efficiency and fairness when logarithmic utility functions are involved. Subject to a given mean revenue for the operator, we study whether it is preferable for a user to pay upon arrival, depending on the congestion level, or whether the user should opt to pay at the end. This leads to a study of the volatility of payment schemes and we show that opting for prepayment is preferable from a user point of view. The analysis yields new results on the asymptotic behavior of conditional response times for processor sharing systems and connections to associated orthogonal polynomials.

scholarly journals Conditional Sojourn times and the volatility of payment schemes for bandwidth sharing in packet networks

2015 ◽  
Vol 52 (4) ◽  
pp. 962-980
Author(s):  
Fabrice M. Guillemin ◽  
Ravi R. Mazumdar
Keyword(s):  
Asymptotic Behavior ◽  
Orthogonal Polynomials ◽  
Response Times ◽  
Point Of View ◽  
Packet Networks ◽  
Processor Sharing ◽  
Bandwidth Sharing ◽  
Conditional Response ◽  
Payment Schemes ◽  
Groves Mechanism

Predictability of revenue and costs to both operators and users is critical for payment schemes. We study the issue of the design of payment schemes in networks with bandwidth sharing. The model we consider is a processor sharing system that is accessed by various classes of users with different processing requirements or file sizes. The users are charged according to a Vickrey–Clarke–Groves mechanism because of its efficiency and fairness when logarithmic utility functions are involved. Subject to a given mean revenue for the operator, we study whether it is preferable for a user to pay upon arrival, depending on the congestion level, or whether the user should opt to pay at the end. This leads to a study of the volatility of payment schemes and we show that opting for prepayment is preferable from a user point of view. The analysis yields new results on the asymptotic behavior of conditional response times for processor sharing systems and connections to associated orthogonal polynomials.

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