Check-in queuing model index calculation method based on backlog carry-over stability approximation

Abstract

The invention provides a check-in queuing model index calculation method based on backlog carry-over stability approximation, and relates to the technical field of check-in services. Firstly, in each time period of check-in queuing time, the passenger arrival rate and the service efficiency of each business are calculated, the business overstock rate is obtained based on the passenger arrival rate and the service efficiency, and the actual total arrival number of the time period is calculated by using the calculated overstock rate of the previous time period and the new arrival number of the current time period; and further calculating the total expected waiting time and the expected waiting queue length of the time period on the basis of the actual number of people accumulated in the previous time period and the handling efficiency, and finally configuring and adjusting check-in service resources according to the prediction indexes. According to the technical scheme, a dynamic and refined resource allocation mechanism is realized, the instantaneous arrival rate is considered, and the influence of historical backlog on the current queuing state is also considered, so that the service capability and the actual passenger flow fluctuation can be more accurately matched, the check-in service resource allocation is convenient to optimize, and the service quality is improved.

Description

Technical Field

[0001] This invention relates to the technical field of check-in services, and more specifically, to a method for calculating the indicators of a check-in queuing model based on a backlog carryover stability approximation. Background Technology

[0002] A queuing system typically consists of four parts: the arrival process, the service process, the number of service counters, and the buffer capacity. In an airport's manual check-in queuing system, each manual check-in counter is essentially the same. For example... Figure 1 As shown, a multi-queue, multi-service-counter modeling approach is generally chosen. After arriving at the manual check-in area, passengers randomly enter a queue at a manual check-in counter to wait for check-in. If the manual check-in counter is free, passengers can immediately receive check-in service; if the manual check-in counter is busy, passengers need to queue in a waiting area, and the waiting area has no length limit. The airport manual check-in queuing process can be abstracted into C queues of two types of passengers. The non-stationary queuing models are composed of parallel connections. The two-class passenger queuing model refers to a queuing system with two classes of passengers, each with different arrival and service times.

[0003] In airport manual check-in queuing systems, passenger arrivals fluctuate significantly within each time period, exhibiting non-stationarity. Furthermore, the arrival intervals between passengers are uncertain, and the number of manual check-in counters is dynamically changing, also exhibiting non-stationarity. The service rate is primarily determined by whether or not passengers are checking in baggage. Therefore, it is necessary to categorize passengers based on whether they are checking in baggage. Simultaneously, airport manual check-in queuing systems may face temporary overload at any time. Therefore, considering the non-stationarity of the check-in queuing model is essential. Summary of the Invention

[0004] To address the problem that existing methods for calculating performance indicators of queuing systems neglect the non-stationarity of arrival time and service rate, making it difficult to reflect the actual queuing situation and hindering the optimal allocation of check-in service resources, this invention proposes a queuing model indicator calculation method based on the backlog carryover stationary approximation. This method considers the non-stationarity of arrival time and service rate in the queuing system model, accurately reflecting the actual queuing situation and performance indicators, thereby optimizing the allocation of check-in service resources and improving service quality.

[0005] To achieve the above-mentioned technical effects, the technical solution of the present invention is as follows: Firstly, this application proposes a method for calculating the index of a check-in queuing model based on the backlog carryover stability approximation, comprising the following steps: S1. Divide the check-in queuing time into several equal-length time periods, and calculate the arrival rate of each type of business and the average processing efficiency of each business in the corresponding time period within each time period. S2. Based on the arrival rate of each type of business within each time period and the average processing efficiency of each type of business within the corresponding time period, calculate the backlog rate of each type of business within each time period; S3. Calculate the actual number of people arriving to handle each type of business in each time period using the number of people arriving to handle each type of business in each time period and the backlog rate of the corresponding business in the previous time period. S4. Using the actual number of people arriving to handle each type of business within each time period and the average processing efficiency of each type of business within the corresponding time period, calculate the overall expected waiting time and the expected waiting line within each time period; S5. Configure check-in service resources based on the total expected waiting time and expected waiting line in each time period.

[0006] In this technical solution, the passenger arrival rate and service efficiency for each service type are calculated within each time period of the check-in queuing time. Based on this, the service backlog rate is derived. Using the calculated backlog rate of the previous time period and the number of new arrivals in the current time period, the actual total number of arrivals in the current time period is calculated. Based on the actual number of arrivals including those from the previous time period and the processing efficiency, the overall expected waiting time and expected waiting line for that time period are further calculated. Finally, check-in service resources are configured and adjusted based on these predicted indicators. This technical solution implements a dynamic and refined resource allocation mechanism. It not only considers the instantaneous arrival rate but also the impact of historical backlogs on the current queuing status, thereby more accurately matching service capacity with actual passenger flow fluctuations to optimize queuing efficiency and passenger experience. This facilitates the optimization of check-in service resource allocation and improves service quality.

[0007] Preferably, the calculation involves determining the arrival rate for each type of service within each time period. λ i and the average processing efficiency of each type of service within the corresponding time period. The calculation expressions are as follows:

[0008] in, Represents the original arrival rate function. Indicates the business category. This indicates the total number of time periods. This represents the original processing efficiency function. This indicates the time span of the specified period.

[0009] Preferably, the process of calculating the backlog rate for each type of business within each time period is as follows: Determine the average processing efficiency of the business Is it greater than the arrival rate for processing this service? If so, then the first The number of people in the backlog during this time period is 0; If not, then calculate the first... Business within a time period backlog ratio ,expression:

[0010] Statistics The number of people in backlog for all categories within a given time period, and the number of people in backlog for the next period. The sum of the backlog numbers for all categories within a given time period is used to obtain the total number of backlog numbers for that time period. .

[0011] Preferably, the calculation expression for the actual number of people arriving to handle each type of business within each time period is:

[0012] in, Indicates the first Business in the previous time period The backlog of people, Indicates the first Actual arrival to handle business within the specified time period The number of people.

[0013] Preferably, the process of calculating the total expected waiting time and the expected waiting line within each time period is as follows: Based on the The actual number of people arriving to handle each type of business within a specific time period. Calculate the actual number of people who arrived to handle all business within that time period. The expression is:

[0014] Based on the The actual number of people arriving to process each type of service within a given time period and the average processing efficiency of each service within the corresponding time period are used to calculate the total number of services in the [number]th time period. Average processing efficiency over a period of time The expression is:

[0015] Based on the The actual number of people who arrived to handle all business within the specified time period and all businesses in Average processing efficiency over a period of time Calculate the first The probability of queuing congestion occurring within a certain time period. The expression is:

[0016] Using the first The probability of queuing congestion occurring within a certain time period. And the actual number of people arriving to handle each type of business during that time period, correct the [number of cases]. The number of arrivals for each service type within a given time period is expressed as follows:

[0017] in, Indicates the first Business within a time period Adjustments for the number of arrivals; Using the corrected first The number of arrivals for each service type within a given time period and the average service efficiency within that time period are used to calculate passenger flow intensity. The expression is:

[0018] Utilizing passenger flow intensity Calculate the first The total expected waiting time within a time period is expressed as follows:

[0019]

[0020] in, The coefficient of variation of the squared distribution of the input process is represented by the following: The coefficient of variation of the squared distribution of the service process is represented by this.

[0021] Preferably, the calculation of the expected waiting queue leader The calculation expression is:

[0022] in, Indicates the first Business within a time period Adjustments for the number of arrivals. Indicates the first Overall expected waiting time within a given time period.

[0023] Preferably, the first The probability of queuing congestion occurring within a certain time period. Let's say it's the probability of loss for Erlang.

[0024] Secondly, this application also proposes a system for calculating the index of a check-in queuing model based on the backlog carryover stationary approximation, the system comprising: The passenger flow and efficiency analysis module is used to divide the check-in queuing time into several equal-length time periods, calculate the arrival rate of each type of business in each time period and the average processing efficiency of each business in the corresponding time period. The service backlog rate calculation module is used to calculate the backlog rate for each type of service within each time period based on the arrival rate of each service and the average processing efficiency of each service within the corresponding time period. The actual service demand calculation module is used to calculate the actual number of people arriving to handle each type of business in each time period by using the number of people arriving to handle each type of business in each time period and the backlog rate of the corresponding business in the previous time period. The queuing status indicator calculation module is used to calculate the overall expected waiting time and expected waiting line in each time period by using the actual number of people arriving to handle each type of business in each time period and the average processing efficiency of each business in the corresponding time period. The service resource dynamic configuration module is used to configure check-in service resources based on the total expected waiting time and expected waiting queue length within each time period.

[0025] Thirdly, this application also proposes a computer device, which includes a memory, a processor, and a computer program stored in the memory that can be run by the processor. The processor executes the computer program to implement the aforementioned method for calculating the index of a check-in queuing model based on a backlog carry-over stability approximation.

[0026] Fourthly, this application also proposes a computer-readable storage medium storing a computer program thereon, the computer program including program instructions, which, when executed by a computer, cause the computer to execute the aforementioned method for calculating the index of a check-in queuing model based on a backlog carry-over stability approximation.

[0027] Compared with the prior art, the beneficial effects of the present invention are: This invention proposes a method for calculating check-in queuing model indicators based on a backlog carryover stationary approximation. First, within each time period of the check-in queuing time, the passenger arrival rate and service efficiency for each service are calculated, and the service backlog rate is derived accordingly. Using the calculated backlog rate from the previous time period and the number of new arrivals in the current time period, the actual total number of arrivals in the current time period is calculated. Based on the actual number of arrivals including those from the previous time period's backlog and processing efficiency, the overall expected waiting time and expected waiting line for that time period are further calculated. Finally, check-in service resources are configured and adjusted based on these predicted indicators. This technical solution implements a dynamic and refined resource allocation mechanism that considers not only the instantaneous arrival rate but also the impact of historical backlogs on the current queuing status. This allows for a more accurate match between service capacity and actual passenger flow fluctuations, optimizing queuing efficiency and passenger experience, facilitating optimized check-in service resource allocation, and improving service quality. Attached Figure Description

[0028] Figure 1 This diagram illustrates the modeling of manual check-in counters as a multi-service counter queuing model proposed in Embodiment 1 of the present invention. Figure 2 This is a flowchart illustrating a method for calculating the index of a queuing model based on a backlog carryover stationary approximation proposed in Embodiment 1 of the present invention. Figure 3 A schematic diagram illustrating the principle of the method for calculating the actual arrival rate based on backlog carryover proposed in Embodiment 2 of the present invention; Figure 4 This is a schematic diagram of the index calculation system for a queuing model based on the backlog carryover stationary approximation proposed in Embodiment 3 of the present invention. Figure 5 This is a schematic diagram of the structure of the computer device proposed in Embodiment 4 of the present invention. Detailed Implementation

[0029] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent. To better illustrate this embodiment, some parts of the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual dimensions; It is understandable to those skilled in the art that some well-known details may be omitted from the accompanying drawings.

[0030] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0031] The positional relationships depicted in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent. Example 1 This embodiment proposes a method for calculating the indicators of a check-in queuing model based on the backlog carryover stationary approximation. A flowchart of this method can be found here. Figure 2 This includes the following steps: S1. Divide the check-in queuing time into several equal-length time periods, and calculate the arrival rate of each type of business and the average processing efficiency of each business in the corresponding time period within each time period. S2. Based on the arrival rate of each type of business within each time period and the average processing efficiency of each type of business within the corresponding time period, calculate the backlog rate of each type of business within each time period; S3. Calculate the actual number of people arriving to handle each type of business in each time period using the number of people arriving to handle each type of business in each time period and the backlog rate of the corresponding business in the previous time period. S4. Using the actual number of people arriving to handle each type of business within each time period and the average processing efficiency of each type of business within the corresponding time period, calculate the overall expected waiting time and the expected waiting line within each time period; S5. Configure check-in service resources based on the total expected waiting time and expected waiting line in each time period.

[0032] In this embodiment, the passenger arrival rate and service efficiency for each service type are first calculated within each time period of the check-in queuing time. Based on this, the service backlog rate is derived. Using the calculated backlog rate of the previous time period and the number of new arrivals in the current time period, the actual total number of arrivals in the current time period is calculated. Based on the actual number of arrivals including those from the previous time period and the processing efficiency, the overall expected waiting time and expected waiting line for that time period are further calculated. Finally, check-in service resources are configured and adjusted based on these predicted indicators. This technical solution implements a dynamic and refined resource allocation mechanism. It not only considers the instantaneous arrival rate but also the impact of historical backlogs on the current queuing status, thereby more accurately matching service capacity with actual passenger flow fluctuations to optimize queuing efficiency and passenger experience, facilitating the optimization of check-in service resource allocation and improving service quality.

[0033] Example 2 In this embodiment, the arrival rate for each type of service is calculated within each time period. λ i and the average processing efficiency of each type of service within the corresponding time period. The calculation expressions are as follows:

[0034] in, Represents the original arrival rate function. Indicates the business category. This indicates the total number of time periods. This represents the original processing efficiency function. This indicates the time span of the specified period.

[0035] Specifically, the original arrival rate function indicates that the arrival rate is not a constant, but a function that varies with time, satisfying a non-homogeneous Poisson process. In this non-homogeneous Poisson process, within the time interval... The probability expression for the arrival of k passengers is:

[0036] Among them, the Indicates the time interval The total number of passengers expected to arrive within the area.

[0037] Specifically, in the original service rate function, the service rate changes over time and follows a super-exponential distribution, assuming that the check-in counter needs to handle a total of X different types of services, and any arriving passenger needs to complete a service. The probability is Each business The service times are independent and follow their own exponential distributions, with a service rate of [missing information]. The total service time obtained probability density function The weighted average of all business transactions is expressed as:

[0038] In this embodiment, the process of calculating the backlog rate for each type of service within each time period is as follows: Determine the average processing efficiency of the business Is it greater than the arrival rate for processing this service? If so, then the first The number of people in the backlog during this time period is 0; If not, then calculate the first... Business within a time period backlog ratio ,expression:

[0039] Statistics The number of people in backlog for all categories within a given time period, and the number of people in backlog for the next period. The sum of the backlog numbers for all categories within a given time period is used to obtain the total number of backlog numbers for that time period. .

[0040] In this embodiment, the calculation expression for the actual number of people arriving to handle each type of business within each time period is:

[0041] in, Indicates the first Business in the previous time period The backlog of people, Indicates the first Actual arrival to handle business within the specified time period The number of people.

[0042] Specifically, the backlog number is calculated based on the backlog rate, and then the actual number of people arriving and processing business is calculated based on the number of people arriving in the current time period. The principle diagram of the number of people is as follows Figure 2 As shown, refer to Figure 2 ,exist During this period, there was no backlog in the previous period. However, because the efficiency of processing the business is lower than the arrival rate of the business, this results in... The backlog rate, and carry over to During this period, therefore During this period, the actual arrival rate is the sum of the arrival rate of this period and the backlog rate of the previous period, expressed as: ,exist The backlog rate generated during this period is carried over to the next period.

[0043] In this embodiment, the process of calculating the total expected waiting time and the expected waiting line within each time period is as follows: Based on the The actual number of people arriving to handle each type of business within a specific time period. Calculate the actual number of people who arrived to handle all business within that time period. The expression is:

[0044] Based on the The actual number of people arriving to process each type of service within a given time period and the average processing efficiency of each service within the corresponding time period are used to calculate the total number of services in the [number]th time period. Average processing efficiency over a period of time The expression is:

[0045] Based on the The actual number of people who arrived to handle all business within the specified time period and all businesses in Average processing efficiency over a period of time Calculate the first The probability of queuing congestion occurring within a certain time period. The expression is:

[0046] Using the first The probability of queuing congestion occurring within a certain time period. And the actual number of people arriving to handle each type of business during that time period, correct the [number of cases]. The number of arrivals for each service type within a given time period is expressed as follows:

[0047] in, Indicates the first Business within a time period Adjustments for the number of arrivals; Using the corrected first The number of arrivals for each service type within a given time period and the average service efficiency within that time period are used to calculate passenger flow intensity. The expression is:

[0048] Utilizing passenger flow intensity Calculate the first Overall expected waiting time within a time period The expression is:

[0049]

[0050] in, The coefficient of variation of the squared distribution of the input process is represented by the following: The coefficient of variation of the squared distribution of the service process is represented by this.

[0051] In this embodiment, the calculation of the expected waiting queue leader... The calculation expression is:

[0052] in, Indicates the first Business within a time period Adjustments for the number of arrivals. Indicates the first Overall expected waiting time within a given time period.

[0053] In this embodiment, the first The probability of queuing congestion occurring within a certain time period. Let's say it's the probability of loss for Erlang.

[0054] Specifically, the Erlang loss probability represents the probability that a newly arrived customer will be blocked.

[0055] Example 3 This embodiment proposes a system for calculating the indicators of a check-in queuing model based on the backlog carryover stationary approximation. In this embodiment, the system is used to implement the method for calculating the indicators of a check-in queuing model based on the backlog carryover stationary approximation. The structural diagram is shown below. Figure 4 As shown, it includes: The passenger flow and efficiency analysis module is used to divide the check-in queuing time into several equal-length time periods, calculate the arrival rate of each type of business in each time period and the average processing efficiency of each business in the corresponding time period. The service backlog rate calculation module is used to calculate the backlog rate for each type of service within each time period based on the arrival rate of each service and the average processing efficiency of each service within the corresponding time period. The actual service demand calculation module is used to calculate the actual number of people arriving to handle each type of business in each time period by using the number of people arriving to handle each type of business in each time period and the backlog rate of the corresponding business in the previous time period. The queuing status indicator calculation module is used to calculate the overall expected waiting time and expected waiting line in each time period by using the actual number of people arriving to handle each type of business in each time period and the average processing efficiency of each business in the corresponding time period. The service resource dynamic configuration module is used to configure check-in service resources based on the total expected waiting time and expected waiting queue length within each time period.

[0056] Example 4 In this embodiment, a computer device is proposed, comprising a memory 101, a processor 102, and a computer program stored in the memory 101 that can be executed by the processor. The processor 102 executes the computer program to implement a method for calculating the indicators of a check-in queuing model based on a backlog carryover stability approximation. A schematic diagram of the device is shown below. Figure 5 As shown.

[0057] Example 5 In this embodiment, a computer-readable storage medium is proposed, on which a computer program is stored. The computer program includes program instructions, which, when executed by a computer, cause the computer to perform the calculation method of the queuing model index based on the backlog carry-over stability approximation as described in Embodiment 1 or Embodiment 2.

[0058] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for calculating the index of a check-in queuing model based on the backlog carryover stationary approximation, characterized in that, Includes the following steps: S1. Divide the check-in queuing time into several equal-length time periods, and calculate the arrival rate of each type of business and the average processing efficiency of each business in the corresponding time period within each time period. S2. Based on the arrival rate of each type of business within each time period and the average processing efficiency of each type of business within the corresponding time period, calculate the backlog rate of each type of business within each time period; S3. Calculate the actual number of people arriving to handle each type of business in each time period using the number of people arriving to handle each type of business in each time period and the backlog rate of the corresponding business in the previous time period. S4. Using the actual number of people arriving to handle each type of business within each time period and the average processing efficiency of each type of business within the corresponding time period, calculate the overall expected waiting time and the expected waiting line within each time period; S5. Configure check-in service resources based on the total expected waiting time and expected waiting line in each time period.

2. The method for calculating the index of the check-in queuing model based on the backlog carryover stationary approximation as described in claim 1, characterized in that, The calculation of the arrival rate for each type of business within each time period. λ i and the average processing efficiency of each type of service within the corresponding time period. The calculation expressions are as follows: in, Represents the original arrival rate function. Indicates the business category. This indicates the total number of time periods. This represents the original processing efficiency function. This indicates the time span of the specified period.

3. The method for calculating the index of the check-in queuing model based on the backlog carryover stationary approximation as described in claim 2, characterized in that, The process for calculating the backlog rate for each type of service within each time period is as follows: Determine the average processing efficiency of the business Is it greater than the arrival rate for processing this service? If so, then the first The number of people in the backlog during this time period is 0; If not, then calculate the first... Business within a time period backlog ratio ,expression: Statistics The number of people in backlog for all categories within a given time period, and the number of people in backlog for the next period. The sum of the backlog numbers for all categories within a given time period gives the total number of backlog numbers for that time period. .

4. The method for calculating the index of the check-in queuing model based on the backlog carryover stationary approximation as described in claim 3, characterized in that, The calculation expression for the actual number of people arriving to handle each type of business within each time period is as follows: in, Indicates the first Business in the previous time period The backlog of people, Indicates the first Actual arrival to handle business within the specified time period The number of people.

5. The method for calculating the index of the check-in queuing model based on the backlog carryover stationary approximation as described in claim 4, characterized in that, The process for calculating the total expected waiting time and expected waiting queue for each time period is as follows: Based on the The actual number of people arriving to handle each type of business within a specific time period. Calculate the actual number of people who arrived to handle all business within that time period. The expression is: Based on the The actual number of people arriving to process each type of service within a given time period and the average processing efficiency of each service within the corresponding time period are used to calculate the total number of services in the [number]th time period. Average processing efficiency over a period of time The expression is: Based on the The actual number of people who arrived to handle all business within the specified time period and all businesses in Average processing efficiency over a period of time Calculate the first The probability of queuing congestion occurring within a certain time period. The expression is: Using the first The probability of queuing congestion occurring within a certain time period. And the actual number of people arriving to handle each type of business during that time period, correct the [number of cases]. The number of arrivals for each service type within a given time period is expressed as follows: in, Indicates the first Business within a time period Adjustments for the number of arrivals; Using the corrected first The number of arrivals for each service type within a given time period and the average service efficiency within that time period are used to calculate passenger flow intensity. The expression is: Utilizing passenger flow intensity Calculate the first Overall expected waiting time within a time period The expression is: in, The coefficient of variation of the squared distribution of the input process is represented by the following: The coefficient of variation of the squared distribution of the service process is represented by this.

6. The method for calculating the index of the check-in queuing model based on the backlog carryover stationary approximation as described in claim 5, characterized in that, The calculation expects the queue leader to wait. The calculation expression is: in, Indicates the first Business within a time period Adjustments for the number of arrivals. Indicates the first Overall expected waiting time within a given time period.

7. The method for calculating the index of the check-in queuing model based on the backlog carryover stationary approximation as described in claim 6, characterized in that, The first The probability of queuing congestion occurring within a certain time period. Let represent the probability of loss for Erlang.

8. A system for calculating the index of a check-in queuing model based on the backlog carryover stationary approximation, characterized in that, The system is used to implement the method according to any one of claims 1 to 7, comprising: The passenger flow and efficiency analysis module is used to divide the check-in queuing time into several equal-length time periods, calculate the arrival rate of each type of business in each time period and the average processing efficiency of each business in the corresponding time period. The service backlog rate calculation module is used to calculate the backlog rate for each type of service within each time period based on the arrival rate of each service and the average processing efficiency of each service within the corresponding time period. The actual service demand calculation module is used to calculate the actual number of people arriving to handle each type of business in each time period by using the number of people arriving to handle each type of business in each time period and the backlog rate of the corresponding business in the previous time period. The queuing status indicator calculation module is used to calculate the overall expected waiting time and expected waiting line in each time period by using the actual number of people arriving to handle each type of business in each time period and the average processing efficiency of each business in the corresponding time period. The service resource dynamic configuration module is used to configure check-in service resources based on the total expected waiting time and expected waiting queue length within each time period.

9. A computer device, characterized in that, The computer device includes a memory, a processor, and a computer program stored in the memory that can be executed by the processor. The processor executes the computer program to implement the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, It stores a computer program, which includes program instructions that, when executed by a computer, cause the computer to perform the method described in any one of claims 1 to 7.

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