scholarly journals Minimizing equilibrium expected sojourn time via performance-based mixed threshold demand allocation in a multiple-server queueing environment

2012 ◽  
Vol 8 (2) ◽  
pp. 299-323 ◽  
Author(s):  
Sin-Man Choi ◽  
◽  
Ximin Huang ◽  
Wai-Ki Ching ◽  
◽  
...  
Keyword(s):  
Sojourn Time ◽  
Expected Sojourn Time ◽  
Demand Allocation

INDIVIDUAL EQUILIBRIUM DYNAMIC ROUTING IN A MULTIPLE SERVER RETRIAL QUEUE

2000 ◽  
Vol 14 (1) ◽  
pp. 9-26 ◽  
Author(s):  
Anthony C. Brooms
Keyword(s):  
Nash Equilibrium ◽  
Poisson Process ◽  
Sojourn Time ◽  
Service System ◽  
Transmission Rate ◽  
Retrial Queue ◽  
Dynamic Learning ◽  
Arrival Times ◽  
The Public ◽  
Expected Sojourn Time

Customers arrive sequentially to a service system where the arrival times form a Poisson process of rate λ. The system offers a choice between a private channel and a public set of channels. The transmission rate at each of the public channels is faster than that of the private one; however, if all of the public channels are occupied, then a customer who commits itself to using one of them attempts to connect after exponential periods of time with mean μ−1. Once connection to a public channel has been made, service is completed after an exponential period of time, with mean ν−1. Each customer chooses one of the two service options, basing its decision on the number of busy channels and reapplying customers, with the aim of minimizing its own expected sojourn time. The best action for an individual customer depends on the actions taken by subsequent arriving customers. We establish the existence of a unique symmetric Nash equilibrium policy and show that its structure is characterized by a set of threshold-type strategies; we discuss the relevance of this concept in the context of a dynamic learning scenario.

Optimal timing of antiviral therapy in HIV infection

1994 ◽  
Vol 31 (A) ◽  
pp. 3-15 ◽  
Author(s):  
Simeon M. Berman
Keyword(s):  
T Cell ◽  
Diffusion Process ◽  
Antiviral Therapy ◽  
Sojourn Time ◽  
First Passage Time ◽  
Passage Time ◽  
Optimal Timing ◽  
Positive Individual ◽  
Expected Sojourn Time

A three-stage real diffusion process is used as a model of the T-cell count of an HIV-positive individual who is to receive antiviral therapy such as AZT. The ‘quality of life' of such a person is identified as the sojourn time of the diffusion process above a certain critical T-cell level c. The time of introducing therapy is defined as the first-passage time of the diffusion to a prescribed level z > c. The distribution of the sojourn time of the diffusion above the level c depends on the level z at which therapy is initiated. The expected sojourn time is explicitly computed as a function of z for the particular diffusion process defining the model. There is a simple criterion for determining when to start therapy as early as possible.

Optimal timing of antiviral therapy in HIV infection

1994 ◽  
Vol 31 (A) ◽  
pp. 3-15 ◽  
Author(s):  
Simeon M. Berman
Keyword(s):  
T Cell ◽  
Diffusion Process ◽  
Antiviral Therapy ◽  
Sojourn Time ◽  
First Passage Time ◽  
Passage Time ◽  
Optimal Timing ◽  
Positive Individual ◽  
Expected Sojourn Time

A three-stage real diffusion process is used as a model of the T-cell count of an HIV-positive individual who is to receive antiviral therapy such as AZT. The ‘quality of life' of such a person is identified as the sojourn time of the diffusion process above a certain critical T-cell level c. The time of introducing therapy is defined as the first-passage time of the diffusion to a prescribed level z > c. The distribution of the sojourn time of the diffusion above the level c depends on the level z at which therapy is initiated. The expected sojourn time is explicitly computed as a function of z for the particular diffusion process defining the model. There is a simple criterion for determining when to start therapy as early as possible.

ASYMPTOTIC PROPERTIES OF SOJOURN TIMES IN MULTICLASS TIME-SHARED SYSTEMS

2008 ◽  
Vol 22 (2) ◽  
pp. 231-259
Author(s):  
Arzad A. Kherani
Keyword(s):  
Sojourn Time ◽  
Busy Period ◽  
Asymptotic Properties ◽  
Tail Behavior ◽  
Queuing Systems ◽  
Conditional Mean ◽  
Sojourn Times ◽  
Heavy Tailed ◽  
Expected Sojourn Time ◽  
Residual Processing

We consider two multiclass discriminatory process sharing (DPS)-like time-shared M/G/1 queuing systems in which the weight assigned to a customer is a function of its class as well as (1) the attained service of the customer in the first system and (2) the residual processing time of the customer in the second system. We study the asymptotic slowdown, the ratio of expected sojourn time to the service requirement, of customers with very large service requirements. We also provide various results dealing with ordering of conditional mean sojourn times of any two given classes. We also show that the sojourn time of an arbitrary customer of a particular class in the standard DPS system (static weights) with heavy-tailed service requirements has a tail behavior similar to that of a customer from the same class that starts a busy period.

A generalization of little's law to moments of queue lengths and waiting times in closed, product-form queueing networks

1989 ◽  
Vol 26 (01) ◽  
pp. 121-133 ◽  
Author(s):  
James McKenna
Keyword(s):  
Sojourn Time ◽  
Queueing Networks ◽  
Waiting Times ◽  
Arrival Rate ◽  
Product Form ◽  
Single Server ◽  
Queue Lengths ◽  
The Mean ◽  
Expected Sojourn Time ◽  
Product Form Queueing Networks

Little's theorem states that under very general conditions L = λW, where L is the time average number in the system, W is the expected sojourn time in the system, and λ is the mean arrival rate to the system. For certain systems it is known that relations of the form E((L) l ) = λ lE((W) l ) are also true, where (L) l = L(L – 1)· ·· (L – l + 1). It is shown in this paper that closely analogous relations hold in closed, product-form queueing networks. Similar expressions relate Nji and Sji, where Nji is the total number of class j jobs at center i and Sji is the total sojourn time of a class j job at center i, when center i is a single-server, FCFS center. When center i is a c-server, FCFS center, Qji and Wji are related this way, where Qji is the number of class j jobs queued, but not in service at center i and Wji is the waiting time in queue of a class j job at center i. More remarkably, generalizations of these results to joint moments of queue lengths and sojourn times along overtake-free paths are shown to hold.

An invariance principle for semi-Markov processes

1985 ◽  
Vol 17 (1) ◽  
pp. 100-126
Author(s):  
D. McDonald
Keyword(s):  
Sojourn Time ◽  
Time Distribution ◽  
Invariant Probability Measure ◽  
Transition Kernel ◽  
Mixing Conditions ◽  
Sojourn Time Distribution ◽  
Semi Markov Process ◽  
Image Position ◽  
Expected Sojourn Time ◽  
Semi Markov Processes

Let (I(t))∞t = () be a semi-Markov process with state space II and recurrent probability transition kernel P. Subject to certain mixing conditions, where Δis an invariant probability measure for P and μb is the expected sojourn time in state b ϵΠ. We show that this limit is robust; that is, for each state b ϵ Πthe sojourn-time distribution may change for each transition, but, as long as the expected sojourn time in b is µb on the average, the above limit still holds. The kernel P may also vary for each transition as long as Δis invariant.

Incentive Effects of Multiple-Server Queueing Networks: The Principal-Agent Perspective

2011 ◽  
Vol 1 (4) ◽  
pp. 379-402 ◽  
Author(s):  
Sin-Man Choi ◽  
Ximin Huang ◽  
Wai-Ki Ching ◽  
Min Huang
Keyword(s):  
Sojourn Time ◽  
Queueing Networks ◽  
Principal Agent ◽  
Queueing Model ◽  
Allocation Scheme ◽  
Service Capacity ◽  
Service Network ◽  
Incentive Effects ◽  
The Common ◽  
Expected Sojourn Time

AbstractA two-server service network has been studied from the principal-agent perspective. In the model, services are rendered by two independent facilities coordinated by an agency, which seeks to devise a strategy to suitably allocate customers to the facilities and to simultaneously determine compensation levels. Two possible allocation schemes were compared — viz. the common queue and separate queue schemes. The separate queue allocation scheme was shown to give more competition incentives to the independent facilities and to also induce higher service capacity. In this paper, we investigate the general case of a multiple-server queueing model, and again find that the separate queue allocation scheme creates more competition incentives for servers and induces higher service capacities. In particular, if there are no severe diseconomies associated with increasing service capacity, it gives a lower expected sojourn time in equilibrium when the compensation level is sufficiently high.

An invariance principle for semi-Markov processes

1985 ◽  
Vol 17 (01) ◽  
pp. 100-126
Author(s):  
D. McDonald
Keyword(s):  
Sojourn Time ◽  
Time Distribution ◽  
Invariant Probability Measure ◽  
Transition Kernel ◽  
Mixing Conditions ◽  
Sojourn Time Distribution ◽  
Semi Markov Process ◽  
Image Position ◽  
Expected Sojourn Time ◽  
Semi Markov Processes

Let (I(t))∞ t = () be a semi-Markov process with state space II and recurrent probability transition kernel P. Subject to certain mixing conditions, where Δis an invariant probability measure for P and μ b is the expected sojourn time in state b ϵΠ. We show that this limit is robust; that is, for each state b ϵ Πthe sojourn-time distribution may change for each transition, but, as long as the expected sojourn time in b is µ b on the average, the above limit still holds. The kernel P may also vary for each transition as long as Δis invariant.

A generalization of little's law to moments of queue lengths and waiting times in closed, product-form queueing networks

1989 ◽  
Vol 26 (1) ◽  
pp. 121-133 ◽  
Author(s):  
James McKenna
Keyword(s):  
Sojourn Time ◽  
Queueing Networks ◽  
Waiting Times ◽  
Arrival Rate ◽  
Product Form ◽  
Single Server ◽  
Queue Lengths ◽  
The Mean ◽  
Expected Sojourn Time ◽  
Product Form Queueing Networks

Little's theorem states that under very general conditions L = λW, where L is the time average number in the system, W is the expected sojourn time in the system, and λ is the mean arrival rate to the system. For certain systems it is known that relations of the form E((L)l) = λ lE((W)l) are also true, where (L)l = L(L – 1)· ·· (L – l + 1). It is shown in this paper that closely analogous relations hold in closed, product-form queueing networks. Similar expressions relate Nji and Sji, where Nji is the total number of class j jobs at center i and Sji is the total sojourn time of a class j job at center i, when center i is a single-server, FCFS center. When center i is a c-server, FCFS center, Qji and Wji are related this way, where Qji is the number of class j jobs queued, but not in service at center i and Wji is the waiting time in queue of a class j job at center i. More remarkably, generalizations of these results to joint moments of queue lengths and sojourn times along overtake-free paths are shown to hold.

scholarly journals A note on the processor-sharing queue in a quasi-reversible network

1983 ◽  
Vol 15 (02) ◽  
pp. 468-469
Author(s):  
Pantelis Tsoucas ◽  
Jean Walrand
Keyword(s):  
Service Time ◽  
Sojourn Time ◽  
Processor Sharing ◽  
Expected Sojourn Time

Consider a processor-sharing queue placed in a quasi-reversible network in equilibrium. This note explains why the expected sojourn time of a customer in such a queue is proportional to his service time.

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